The value of ${(3^{m})}^{n}$ , for every pair of integers $(m, n)$ is

3^{m + n}

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3^{m n}

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3^{m^{n}}

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3^{m} + 3^{n}

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Solution

The correct option is B $3^{m n}$
We know that for some positive integers $m$ and $n$ ,
${(x^{m})}^{n} = x^{m \times n} = x^{m n}$
Therefore, ${(3^{m})}^{n} = 3^{m \times n} = 3^{m n}$
Hence, the value of ${(3^{m})}^{n}$ is $3^{m n}$ .

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