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

The solution to (2x^2y^{-3})^{-2} is (y^6)/(4x^4)

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

simplify

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

\frac{y ^{6}}{4 x ^{4}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(2 x^{2} y^{- 3})^{2} : \frac{4 x ^{4}}{y ^{6}}

= \frac{1}{\frac{4 x ^{4}}{y ^{6}}}

Apply the fraction rule:

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

= \frac{y ^{6}}{4 x ^{4}}

\frac{1}{25} + \frac{( 25 x ^{4} )}{36} - \frac{( x ^{2} )}{3}

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6 x - 2 y + 7 - (2 x + 3)

(7 \cdot x^{3 n - 2} - 5) (7 \cdot x^{3 n - 2} + 9)

4 x^{2} - 9 y^{2} + 20 x + 25