What is (3m^{-2}n^4)^{-2} ?

The solution to (3m^{-2}n^4)^{-2} is (m^4)/(9n^8)

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simplify (3m^{-2}n^4)^{-2}

simplify

(3 m^{- 2} n^{4})^{- 2}

\frac{m ^{4}}{9 n ^{8}}

Solution steps

(3 m^{- 2} n^{4})^{- 2}

Apply exponent rule:

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

(3 m^{- 2} n^{4})^{- 2} = \frac{1}{( 3 m ^{- 2} n ^{4} ) ^{2}}

= \frac{1}{( 3 m ^{- 2} n ^{4} ) ^{2}}

Simplify

(3 m^{- 2} n^{4})^{2} : \frac{9 n ^{8}}{m ^{4}}

= \frac{1}{\frac{9 n ^{8}}{m ^{4}}}

Apply the fraction rule:

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

= \frac{m ^{4}}{9 n ^{8}}

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