Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$\sqrt{x^{3} y^{-2}}$

Given:

$\sqrt{x^{3} y^{-2}}$

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,

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

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

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

$=\frac{x^{\frac{3}{2}}}{y}$

Hence, $\sqrt{x^{3} y^{-2}}=\frac{x^{\frac{3}{2}}}{y}$. 

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Updated on: 10-Oct-2022

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