Simplify:$ \left(16^{-1 / 5}\right)^{5 / 2} $

Given:

\( \left(16^{-1 / 5}\right)^{5 / 2} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$(16^{-1 / 5})^{5 / 2}=[[2^{4}]^{\frac{-1}{5}}]^{\frac{5}{2}}$

$=2^{4 \times \frac{-1}{5} \times \frac{5}{2}}$

$=2^{-2}$

$=\frac{1}{2^{2}}$

$=\frac{1}{4}$

Hence, $(16^{-1 / 5})^{5 / 2}=\frac{1}{4}$.

Tutorialspoint

Updated on: 10-Oct-2022

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