INTRODUCTION Do you know what the mass of earth is? It is 5,970,000,000,000,000,000,000,000 kg! Can you read this number? Mass of Uranus is 86,800,000,000,000,000,000,000,000 kg. Which
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EXPONENTS We can write large numbers in a shorter form using exponents. Observe 10, 000 = 10 × 10 × 10 × 10 = 104 The short notation 1
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LAWS OF EXPONENTS Multiplying Powers with the Same Base: (i) Let us calculate 22 × 23 2 2 × 23 = (2 × 2) × (2 × 2 × 2) &
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Dividing Powers with the Same Base Let us simplify 37 ÷ 34 ? \({{3}^{7}}\div {{3}^{4}}=\frac{{{3}^{7}}}{{{3}^{4}}}=\frac{3\text{ }\times 3\times 3\times 3\times 3\times 3\times 3}{3\text{
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Taking Power of a Power Consider the following Simplify \({{({{2}^{3}})}^{2}};{{({{3}^{2}})}^{4}}\) Now, \({{({{2}^{3}})}^{2}}\) means 23 is multiplied two times with itself. \({{({
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Multiplying Powers with the Same Exponents Can you simplify 23 × 33 ? Notice that here the two terms 23 and 33 have different bases, but the same exponents. Now, 2 3 × 33 = (2
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Dividing Powers with the Same Exponents Observe the following simplifications: (i)\(\frac{{{2}^{4}}}{{{3}^{4}}}=\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}=\frac{2}{3}\times \fra
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MISCELLANEOUS EXAMPLES USING THE LAWS OF EXPONENTS Let us solve some examples using rules of exponents developed. EXAMPLE Write exponential form for 8 × 8 × 8 × 8 taking
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DECIMAL NUMBER SYSTEM Let us look at the expansion of 47561, which we already know: 47561 = 4 × 10000 + 7 × 1000 + 5 × 100 + 6 × 10 + 1 We can express it using powe
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EXPRESSING LARGE NUMBERS IN THE STANDARD FORM Let us now go back to the beginning of the chapter. We said that large numbers can be conveniently expressed using exponents. We have not as yet shown
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