What is ((2x^2)/(5y^4))^{-2} ?

The solution to ((2x^2)/(5y^4))^{-2} is (25y^8)/(4x^4)

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simplify ((2x^2)/(5y^4))^{-2}

simplify

(\frac{2 x ^{2}}{5 y ^{4}})^{- 2}

\frac{25 y ^{8}}{4 x ^{4}}

Solution steps

(\frac{2 x ^{2}}{5 y ^{4}})^{- 2}

Apply exponent rule:

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

(\frac{2 x ^{2}}{5 y ^{4}})^{- 2} = \frac{1}{( \frac{2 x ^{2}}{5 y ^{4}} ) ^{2}}

= \frac{1}{( \frac{2 x ^{2}}{5 y ^{4}} ) ^{2}}

Simplify

(\frac{2 x ^{2}}{5 y ^{4}})^{2} : \frac{4 x ^{4}}{25 y ^{8}}

= \frac{1}{\frac{4 x ^{4}}{25 y ^{8}}}

Apply the fraction rule:

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

= \frac{25 y ^{8}}{4 x ^{4}}

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(\frac{12 p ^{\frac{3}{2}}}{15 p})^{4}

What is ((2x^2)/(5y^4))^{-2} ?
The solution to ((2x^2)/(5y^4))^{-2} is (25y^8)/(4x^4)