Question

Evaluate : (64^-1/5)^5/2​

Answer 1

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Answer 2

${( {64}^{ - \frac{1}{5} } )}^{ \frac{5}{2} } \\ \\ \bf using \: the \: identity : \\ {( {a}^{m} )}^{n} = {a}^{m \times n} \\ \\ = {64}^{ - \frac{1}{5} \times \frac{5}{2} } \\ \\ = {64}^{ - \frac{1}{2} } \\ \\ \bf using \: the \: identity : \\ {a}^{ - m} = \frac{1}{ {a}^{m} } \\ \\ = \frac{1}{ {64}^{ \frac{1}{2} } } \\ \\ = \frac{1}{ {( {8}^{2} )}^{ \frac{1}{2} } } \\ \\ = \frac{1}{ {8}^{2 \times \frac{1}{2} } } \\ \\ \bf = \frac{1}{8}$

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