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Power of a Power

If b = √ a ...

Question

If $b = \sqrt[n]{a^{m}}$ , then will $a = \sqrt[m]{b^{n}}$ .

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Solution

$b = \sqrt[n]{a^{m}} = a^{m / n} ⟹ a = b^{n / m} = \sqrt[m]{b^{n}}$

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