What is (5z^{-3}*y^3*z^{-7})^{-1} ?

The solution to (5z^{-3}*y^3*z^{-7})^{-1} is (z^{10})/(5y^3)

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simplify (5z^{-3}y^3z^{-7})^{-1}

simplify

(5 z^{- 3} \cdot y^{3} \cdot z^{- 7})^{- 1}

\frac{z ^{10}}{5 y ^{3}}

Solution steps

(5 z^{- 3} y^{3} z^{- 7})^{- 1}

Apply exponent rule:

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

(5 z^{- 3} y^{3} z^{- 7})^{- 1} = \frac{1}{5 z ^{- 3} y ^{3} z ^{- 7}}

= \frac{1}{5 z ^{- 3} y ^{3} z ^{- 7}}

5 z^{- 3} y^{3} z^{- 7} = 5 z^{- 10} y^{3}

= \frac{1}{5 z ^{- 10} y ^{3}}

Multiply

5 y^{3} z^{- 10} : \frac{5 y ^{3}}{z ^{10}}

= \frac{1}{\frac{5 y ^{3}}{z ^{10}}}

Apply the fraction rule:

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

= \frac{z ^{10}}{5 y ^{3}}

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What is (5z^{-3}*y^3*z^{-7})^{-1} ?
The solution to (5z^{-3}*y^3*z^{-7})^{-1} is (z^{10})/(5y^3)