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

The solution to (((3a^2))/((a^{-2)*b^3*c^2)})^{-2} is (b^6c^4)/(9a^8)

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

simplify

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

\frac{b ^{6} c ^{4}}{9 a ^{8}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(\frac{3 a ^{2}}{a ^{- 2} b ^{3} c ^{2}})^{2} : \frac{9 a ^{8}}{b ^{6} c ^{4}}

= \frac{1}{\frac{9 a ^{8}}{b ^{6} c ^{4}}}

Apply the fraction rule:

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

= \frac{b ^{6} c ^{4}}{9 a ^{8}}

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What is (((3a^2))/((a^{-2)*b^3*c^2)})^{-2} ?
The solution to (((3a^2))/((a^{-2)*b^3*c^2)})^{-2} is (b^6c^4)/(9a^8)