The correct option is B (3/5 )^16 Given, (5/3 )^ 2×(5/3 )^ 14 Using law of exponents, a^m × a^n = (a)^m+n ⇒(5/3 )^ 2 14 ⇒(5/3 )^ 16 ⇒(3/5 )^16 ...

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Product Law

Evaluate5/3-2...

Question

Evaluate
${(\frac{5}{3})}^{- 2} \times {(\frac{5}{3})}^{- 14}$

${(\frac{3}{5})}^{- 16}$

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${(\frac{3}{5})}^{16}$

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${(\frac{5}{3})}^{16}$

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${(\frac{5}{3})}^{- 16}$

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Solution

The correct option is B
${(\frac{3}{5})}^{16}$

$G i v e n, {(\frac{5}{3})}^{- 2} \times {(\frac{5}{3})}^{- 14}$

Using law of exponents, $a^{m} \times a^{n} = (a)^{m + n}$

$\Rightarrow {(\frac{5}{3})}^{- 2 - 14}$
$\Rightarrow {(\frac{5}{3})}^{- 16}$
$\Rightarrow {(\frac{3}{5})}^{16}$

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