{"id":1955,"date":"2026-05-23T10:50:47","date_gmt":"2026-05-23T10:50:47","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1955"},"modified":"2026-05-23T10:51:37","modified_gmt":"2026-05-23T10:51:37","slug":"ncert-class-8-maths-power-play-solutions-guide","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-8-maths-power-play-solutions-guide\/","title":{"rendered":"NCERT Class 8 Maths Power Play Solutions Guide"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter <strong>\u201cPower Play\u201d<\/strong> introduces students to the fascinating world of exponents, exponential growth, scientific notation, powers of 10, and large numbers. Through interesting real-life examples like folding paper, magical ponds, password combinations, and huge world statistics, students learn how powers simplify calculations and help represent extremely large or small numbers.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Particular<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Chapter Name<\/td><td>Power Play<\/td><\/tr><tr><td>Class<\/td><td>Grade 8<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Main Topics<\/td><td>Exponents, Powers, Scientific Notation<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Important For<\/td><td>School Exams, Olympiads<\/td><\/tr><tr><td>Skills Developed<\/td><td>Logical Thinking, Estimation, Number Sense<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exponential Growth<\/li>\n\n\n\n<li>Exponential Notation<\/li>\n\n\n\n<li>Laws of Exponents<\/li>\n\n\n\n<li>Negative Exponents<\/li>\n\n\n\n<li>Powers of 10<\/li>\n\n\n\n<li>Scientific Notation<\/li>\n\n\n\n<li>Large Numbers<\/li>\n\n\n\n<li>Linear vs Exponential Growth<\/li>\n\n\n\n<li>Estimation &amp; Approximation<\/li>\n\n\n\n<li>Real-life Applications of Powers<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Exponential Form<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mi>a<\/mi><\/msup><mo>=<\/mo><mi>n<\/mi><mo>\u00d7<\/mo><mi>n<\/mi><mo>\u00d7<\/mo><mi>n<\/mi><mo>\u22ef<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">n^a=n\\times n\\times n\\cdots<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Product Rule<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mi>a<\/mi><\/msup><mo>\u00d7<\/mo><msup><mi>n<\/mi><mi>b<\/mi><\/msup><mo>=<\/mo><msup><mi>n<\/mi><mrow><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">n^a\\times n^b=n^{a+b}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Quotient Rule<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><msup><mi>n<\/mi><mi>a<\/mi><\/msup><msup><mi>n<\/mi><mi>b<\/mi><\/msup><\/mfrac><mo>=<\/mo><msup><mi>n<\/mi><mrow><mi>a<\/mi><mo>\u2212<\/mo><mi>b<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{n^a}{n^b}=n^{a-b}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Power of a Power<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mi>a<\/mi><\/msup><msup><mo stretchy=\"false\">)<\/mo><mi>b<\/mi><\/msup><mo>=<\/mo><msup><mi>n<\/mi><mrow><mi>a<\/mi><mi>b<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(n^a)^b=n^{ab}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Negative Exponent<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mrow><mo>\u2212<\/mo><mi>a<\/mi><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><msup><mi>n<\/mi><mi>a<\/mi><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">n^{-a}=\\frac{1}{n^a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Scientific Notation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>\u00d7<\/mo><msup><mn>10<\/mn><mi>y<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x\\times10^y<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-Step Solutions<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">2.1 Experiencing the Power Play<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. What happens to the thickness after every fold?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The thickness doubles after every fold.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Initial thickness = 0.001 cm<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After first fold:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0.001<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mn>0.002<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0.001\\times2=0.002<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After second fold:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0.001<\/mn><mo>\u00d7<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>0.004<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0.001\\times2^2=0.004<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The thickness becomes double after every fold.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is the thickness after 30 folds?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using exponential growth:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0.001<\/mn><mo>\u00d7<\/mo><msup><mn>2<\/mn><mn>30<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">0.001\\times2^{30}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Approximate value:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2248 10.7 km<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The thickness after 30 folds is about 10.7 km.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Why is this called exponential growth?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The quantity increases by repeated multiplication instead of repeated addition.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After every fold:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00d72 growth occurs.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This is called exponential growth because the thickness multiplies repeatedly.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">2.2 Exponential Notation and Operations<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Express the following in exponential form<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(i) 6 \u00d7 6 \u00d7 6 \u00d7 6<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>6<\/mn><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">6^4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">6\u2074<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) y \u00d7 y<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>y<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">y^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">y\u00b2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) b \u00d7 b \u00d7 b \u00d7 b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>b<\/mi><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">b^4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">b\u2074<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv) 5 \u00d7 5 \u00d7 7 \u00d7 7 \u00d7 7<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>7<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">5^2\\times7^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">5\u00b2 \u00d7 7\u00b3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. Express 648 in exponential prime factor form<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Prime factorisation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">648 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>648<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">648=2^3\\times3^4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2\u00b3 \u00d7 3\u2074<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q6. Find the value of:<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2\\times10^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 2 \u00d7 1000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 2000<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2000<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>7<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">7^2\\times2^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 49 \u00d7 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 392<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">392<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">The Stones that Shine<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q7. How many diamonds were there?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Each level multiplies by 3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total diamonds:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>3<\/mn><mn>7<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">3^7<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 2187<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2187 diamonds.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Laws of Exponents<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q8. Simplify:<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>p<\/mi><mn>4<\/mn><\/msup><mo>\u00d7<\/mo><msup><mi>p<\/mi><mn>6<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">p^4\\times p^6<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using product law:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>p<\/mi><mrow><mn>4<\/mn><mo>+<\/mo><mn>6<\/mn><\/mrow><\/msup><mo>=<\/mo><msup><mi>p<\/mi><mn>10<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">p^{4+6}=p^{10}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">p\u00b9\u2070<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q9. Write 2\u00b9\u2070 as power of power<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>10<\/mn><\/msup><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><msup><mn>2<\/mn><mn>5<\/mn><\/msup><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^{10}=(2^5)^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Also,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>10<\/mn><\/msup><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><msup><mo stretchy=\"false\">)<\/mo><mn>5<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^{10}=(2^2)^5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">(2\u2075)\u00b2 and (2\u00b2)\u2075<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Magical Pond<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q10. If pond becomes full on 30th day, when was it half full?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Since the lotuses double every day:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Half full = one day earlier.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">29th day.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q11. Compute:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>5<\/mn><mn>5<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^5\\times5^5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>m<\/mi><mi>a<\/mi><\/msup><mo>\u00d7<\/mo><msup><mi>n<\/mi><mi>a<\/mi><\/msup><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>m<\/mi><mi>n<\/mi><msup><mo stretchy=\"false\">)<\/mo><mi>a<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">m^a\\times n^a=(mn)^a<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= (2 \u00d7 5)\u2075<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 10\u2075<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">10\u2075<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">How Many Combinations<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q12. How many passwords are possible in a 5-digit lock?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Each slot has 10 choices.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total combinations:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>10<\/mn><mn>5<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">10^5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 100000<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1,00,000 passwords.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">2.3 The Other Side of Powers<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q13. Find:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>\u00f7<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^4\\div2^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using quotient rule:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mrow><mn>4<\/mn><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>=<\/mo><msup><mn>2<\/mn><mn>1<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^{4-3}=2^1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q14. What is:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>0<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Any non-zero number raised to zero is 1.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q15. Find:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mrow><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^{-6}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using negative exponent rule:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mrow><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mn>6<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">2^{-6}=\\frac1{2^6}<\/annotation><\/semantics><\/math>\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 1\/64<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1\/64<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">2.4 Powers of 10<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q16. Write 47561 using powers of 10<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>4<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>7<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>1<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>0<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(4\\times10^4)+(7\\times10^3)+(5\\times10^2)+(6\\times10^1)+(1\\times10^0)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(4 \u00d7 10\u2074) + (7 \u00d7 10\u00b3) + (5 \u00d7 10\u00b2) + (6 \u00d7 10\u00b9) + (1 \u00d7 10\u2070)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Scientific Notation<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q17. Express 5900 in scientific notation<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5900<\/mn><mo>=<\/mo><mn>5.9<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">5900=5.9\\times10^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">5.9 \u00d7 10\u00b3<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q18. Express 34,30,000 in standard form<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3430000<\/mn><mo>=<\/mo><mn>3.43<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>6<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">3430000=3.43\\times10^6<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">3.43 \u00d7 10\u2076<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Large Numbers<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q19. Estimated population of ants<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>16<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2\\times10^{16}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2 \u00d7 10\u00b9\u2076 ants globally.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Confusing multiplication with powers<\/li>\n\n\n\n<li>Forgetting exponent rules<\/li>\n\n\n\n<li>Writing incorrect scientific notation<\/li>\n\n\n\n<li>Ignoring negative exponent meaning<\/li>\n\n\n\n<li>Wrong prime factorisation<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Memorise exponent laws carefully<\/li>\n\n\n\n<li>Practice scientific notation daily<\/li>\n\n\n\n<li>Revise powers of 10 frequently<\/li>\n\n\n\n<li>Solve estimation-based questions<\/li>\n\n\n\n<li>Learn real-life applications of exponents<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. What is 2\u2075?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A. 10<br>B. 25<br>C. 32<br>D. 64<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C. 32<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. Which is equal to 10\u2075?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A. 1000<br>B. 10000<br>C. 100000<br>D. 1000000<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C. 100000<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. Simplify:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">3^2\\times3^4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. 3\u2076<br>B. 9\u2076<br>C. 3\u2078<br>D. 6\u00b3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 3\u2076<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. What is exponential growth?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Growth that happens through repeated multiplication.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is scientific notation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A method of writing large numbers using powers of 10.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What is the value of any number raised to zero?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">1<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. What is a negative exponent?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It represents reciprocal values.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. What is the formula for multiplying powers?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mi>a<\/mi><\/msup><mo>\u00d7<\/mo><msup><mi>n<\/mi><mi>b<\/mi><\/msup><mo>=<\/mo><msup><mi>n<\/mi><mrow><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">n^a\\times n^b=n^{a+b}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udcd8 Get complete NCERT Solutions, Mock Tests, Practice Questions, and Exam Preparation Resources at:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a>www.mymockmate.com<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\ude80 Practice smarter with All India Mock Tests and Instant Results.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p>Short Introduction The chapter \u201cPower Play\u201d introduces students to the fascinating world of exponents, exponential growth, scientific notation,<\/p>\n","protected":false},"author":1,"featured_media":1956,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_angie_page":false,"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"page_builder":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[119,105,121],"tags":[497,458,457,465,487,489,484,496,470,490,493,464,475,494,483,491,482,488,485,495,486,492,463],"class_list":["post-1955","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-8","category-maths-class-8","category-power-play","tag-cbse-class-8-maths","tag-cbse-maths-solutions","tag-class-8-mathematics","tag-exam-preparation","tag-exponential-growth","tag-exponential-notation","tag-exponents-and-powers","tag-exponents-rules","tag-grade-8-maths","tag-large-numbers","tag-maths-chapter-2","tag-maths-mcqs","tag-maths-practice-questions","tag-ncert-maths-guide","tag-ncert-solutions-class-8-maths","tag-negative-exponents","tag-power-play-class-8","tag-power-play-solutions","tag-powers-of-10","tag-scientific-form","tag-scientific-notation","tag-standard-form","tag-step-by-step-solutions"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=1955"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1955\/revisions"}],"predecessor-version":[{"id":1957,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1955\/revisions\/1957"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1956"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}