What is (x^{1/2}y^{-1/4}z)^{-2} ?

The solution to (x^{1/2}y^{-1/4}z)^{-2} is (y^{1/2})/(xz^2)

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simplify (x^{1/2}y^{-1/4}z)^{-2}

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(x^{\frac{1}{2}} y^{- \frac{1}{4}} z)^{- 2} = \frac{1}{( x ^{\frac{1}{2}} y ^{- \frac{1}{4}} z ) ^{2}}

= \frac{1}{( x ^{\frac{1}{2}} y ^{- \frac{1}{4}} z ) ^{2}}

Simplify

(x^{\frac{1}{2}} y^{- \frac{1}{4}} z)^{2} : \frac{x z ^{2}}{y ^{\frac{1}{2}}}

= \frac{1}{\frac{x z ^{2}}{y ^{\frac{1}{2}}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{y ^{\frac{1}{2}}}{x z ^{2}}

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What is (x^{1/2}y^{-1/4}z)^{-2} ?
The solution to (x^{1/2}y^{-1/4}z)^{-2} is (y^{1/2})/(xz^2)