Simplify by using the law of exponents-i 76 - 36ii 43 - 23 - 53-2-

(i) 7^6 × 3^6=(7 × 3)^6=21^6 [Since, a^m × b^m=(a × b)^m ] lt;!–td border: 1px solid #cccccc;br mso data placement:same cell;– gt; [1] (ii) 4^3 × 2^3 × 5^ ...

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Byju's Answer

Standard VII

Mathematics

Exponent Numbers with Different Base and Same Power

Simplify by u...

Question

Simplify by using the law of exponents.
(i) $7^{6} \times 3^{6}$
(ii) $4^{3} \times 2^{3} \times 5^{3}$ $[2]$

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Solution

(i) $7^{6} \times 3^{6} = (7 \times 3)^{6} = 21^{6}$
[Since, $a^{m} \times b^{m} = (a \times b)^{m}$ ]
 $[1]$
(ii) $4^{3} \times 2^{3} \times 5^{3} = (4 \times 2 \times 5)^{3} = 40^{3}$
[Rule extended for 3 numbers]
 $[1]$

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(\frac{3}{2} \times \frac{1}{6}) + (\frac{5}{3} \times \frac{7}{2}) - (\frac{13}{8} \times \frac{4}{3})

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(\frac{1}{4} \times \frac{2}{7}) - (\frac{5}{14} \times \frac{- 2}{3}) + (\frac{3}{7} \times \frac{9}{2})

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(\frac{13}{9} \times \frac{- 15}{2}) + (\frac{7}{3} \times \frac{8}{5}) + (\frac{3}{5} \times \frac{1}{2})

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Q. Find the product.
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Simplify by using the law of exponents. (i) 76×36 (ii) 43×23×53 [2]

(i) 76×36=(7×3)6=216 [Since, am×bm=(a×b)m ]  [1] (ii) 43×23×53=(4×2×5)3=403 [Rule extended for 3 numbers]  [1]

Simplify by using the law of exponents.
(i) $7^{6} \times 3^{6}$
(ii) $4^{3} \times 2^{3} \times 5^{3}$ $[2]$