Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$\left(x^{-2 / 3} y^{-1 / 2}\right)^{2}$

Given:

$\left(x^{-2 / 3} y^{-1 / 2}\right)^{2}$

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,

$(x^{\frac{-2}{3}} y^{\frac{-1}{2}})^{2}=x^{\frac{-2}{3} \times 2} \times y^{\frac{-1}{2} \times 2}$

$=(x)^{\frac{-4}{3}} \times y^{-1}$

$=\frac{1}{x^{\frac{4}{3}}y}$

Hence, $(x^{-2 / 3} y^{-1 / 2})^{2}=\frac{1}{x^{\frac{4}{3}}y}$.  

Tutorialspoint

Updated on: 10-Oct-2022

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