Express ${[{(- 3)}^{5}]}^{3}$ with a single exponent.

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Solution

As we know that for any non-zero integer $' a'$ and natural numbers $m$ and $n$ , we have,
${(a^{m})}^{n} = a^{m n}$ .
So, on applying, we get , ${[{(- 3)}^{5}]}^{3}$ $= {(- 3)}^{5 \times 3} = {(- 3)}^{15}$
Hence, ${[{(- 3)}^{5}]}^{3}$ as a single exponent will be equal to ${(- 3)}^{15}$ .

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