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

The solution to (3x^2y^{-2})^{-2} is (y^4)/(9x^4)

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

simplify

(3 x^{2} y^{- 2})^{- 2}

\frac{y ^{4}}{9 x ^{4}}

Solution steps

(3 x^{2} y^{- 2})^{- 2}

Apply exponent rule:

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

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

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

Simplify

(3 x^{2} y^{- 2})^{2} : \frac{9 x ^{4}}{y ^{4}}

= \frac{1}{\frac{9 x ^{4}}{y ^{4}}}

Apply the fraction rule:

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

= \frac{y ^{4}}{9 x ^{4}}

5 a^{- 8} b^{4}

\frac{18 c ^{5}}{16 c ^{3}}

7^{- 4} \cdot 7 \cdot 7^{3}

- 9 x^{3} y^{2} (- 13 x^{2} y^{5})