What is 2(a^2b^{-3})^{-2} ?

The solution to 2(a^2b^{-3})^{-2} is (2b^6)/(a^4)

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simplify 2(a^2b^{-3})^{-2}

simplify

2 (a^{2} b^{- 3})^{- 2}

\frac{2 b ^{6}}{a ^{4}}

Solution steps

2 (a^{2} b^{- 3})^{- 2}

Apply exponent rule:

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

(a^{2} b^{- 3})^{- 2} = \frac{1}{( a ^{2} b ^{- 3} ) ^{2}}

= 2 \cdot \frac{1}{( a ^{2} b ^{- 3} ) ^{2}}

Simplify

(a^{2} b^{- 3})^{2} : \frac{a ^{4}}{b ^{6}}

= 2 \cdot \frac{1}{\frac{a ^{4}}{b ^{6}}}

Apply the fraction rule:

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

= 2 \cdot \frac{b ^{6}}{a ^{4}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 b ^{6}}{a ^{4}}

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