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Monomial

Simplify : ...

Question

Simplify : ${(x^{- 2 / 3} y^{- 1 / 2})}^{2}$

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Solution

${(x^{\frac{- 2}{3}} y^{\frac{- 1}{2}})}^{2}$
$= {(x^{\frac{- 2}{3}})}^{2} {(y^{\frac{- 1}{2}})}^{2}$ since ${(a b)}^{m} = a^{m} b^{m}$
$= x^{\frac{- 1}{3}} y^{- 1}$
$= \frac{1}{x^{\frac{1}{3}} y}$ since $a^{- m} = \frac{1}{a^{m}}$

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