Question

Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2? StartFraction x Superscript one-half baseline Over y z squared EndFraction StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction StartFraction y Superscript one-half Baseline Over x z squared EndFraction

Answer 1

Answer:

$\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}$

Step-by-step explanation:

Given

$x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}$

Required

Find the equivalent

To find the equivalent of the given expression; we have to apply laws of indices;

As a law;

$a^{-m} = \frac{1}{a^m}$

So; the expression $x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}$ becomes

$x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}}*\frac{1}{z^2}$

This is further simplified to

$x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}} * z^2}$

$x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}z^2}$

Combine to form a single fraction

$\frac{x^{\frac{1}{2}}*1}{y^{\frac{1}{4}}z^2}$

Multiply numerator

$\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}$

The expression can not be further simplified

Hence $x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}$ is equivalent to $\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}$