If ${[{(\frac{- 7}{3})}^{2}]}^{5}$ can be expressed as a rational number with negative exponent as ${(\frac{- 3}{7})}^{- m}$ , then the value of $(- m)$ is?

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Solution

The value of ${[{(\frac{- 7}{3})}^{2}]}^{5}$
$= {(\frac{- 7}{3})}^{10}$
$= {(\frac{- 3}{7})}^{- 10}$ ....As ${(\frac{m}{n})}^{n} = {(\frac{n}{m})}^{- n}$
Comparing this with ${(\frac{- 3}{7})}^{- m}$ , we get $m = 10$

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