What is ((12x^3y^2z)/(3x^{-2)y^6z^8})^{-2} ?

The solution to ((12x^3y^2z)/(3x^{-2)y^6z^8})^{-2} is (y^8z^{14})/(16x^{10)}

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simplify ((12x^3y^2z)/(3x^{-2)y^6z^8})^{-2}

simplify

(\frac{12 x ^{3} y ^{2} z}{3 x ^{- 2} y ^{6} z ^{8}})^{- 2}

\frac{y ^{8} z ^{14}}{16 x ^{10}}

Solution steps

(\frac{12 x ^{3} y ^{2} z}{3 x ^{- 2} y ^{6} z ^{8}})^{- 2}

Apply exponent rule:

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

(\frac{12 x ^{3} y ^{2} z}{3 x ^{- 2} y ^{6} z ^{8}})^{- 2} = \frac{1}{( \frac{12 x ^{3} y ^{2} z}{3 x ^{- 2} y ^{6} z ^{8}} ) ^{2}}

= \frac{1}{( \frac{12 x ^{3} y ^{2} z}{3 x ^{- 2} y ^{6} z ^{8}} ) ^{2}}

Simplify

(\frac{12 x ^{3} y ^{2} z}{3 x ^{- 2} y ^{6} z ^{8}})^{2} : \frac{16 x ^{10}}{y ^{8} z ^{14}}

= \frac{1}{\frac{16 x ^{10}}{y ^{8} z ^{14}}}

Apply the fraction rule:

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

= \frac{y ^{8} z ^{14}}{16 x ^{10}}

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What is ((12x^3y^2z)/(3x^{-2)y^6z^8})^{-2} ?
The solution to ((12x^3y^2z)/(3x^{-2)y^6z^8})^{-2} is (y^8z^{14})/(16x^{10)}