Express ${(5^{3})}^{4}$ 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 , ${(5^{3})}^{4}$ $= 5^{3 \times 4} = 5^{12}$
Hence, ${(5^{3})}^{4}$ as a single exponent will be equal to $5^{12}$ .

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