What is (((3x^{3/2}y^3))/((x^2y^{-1/2))})^{-2} ?

The solution to (((3x^{3/2}y^3))/((x^2y^{-1/2))})^{-2} is x/(9y^7)

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simplify (((3x^{3/2}y^3))/((x^2y^{-1/2))})^{-2}

simplify

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

\frac{x}{9 y ^{7}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(\frac{3 x ^{\frac{3}{2}} y ^{3}}{x ^{2} y ^{- \frac{1}{2}}})^{2} : \frac{9 y ^{7}}{x}

= \frac{1}{\frac{9 y ^{7}}{x}}

Apply the fraction rule:

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

= \frac{x}{9 y ^{7}}

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What is (((3x^{3/2}y^3))/((x^2y^{-1/2))})^{-2} ?
The solution to (((3x^{3/2}y^3))/((x^2y^{-1/2))})^{-2} is x/(9y^7)