Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$(\sqrt{x^{-3}})^{5}$

Given:

$(\sqrt{x^{-3}})^{5}$

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,

$(\sqrt{x^{-3}})^{5}=(x^{\frac{-3}{2}})^5$

$=(x)^{\frac{-3}{2}\times5}$

$=(x)^{\frac{-15}{2}}$

$=\frac{1}{(x)^{\frac{15}{2}}}$

Hence, $(\sqrt{x^{-3}})^{5}=\frac{1}{(x)^{\frac{15}{2}}}$.

Tutorialspoint

Updated on: 10-Oct-2022

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