What is ((9m^4n^{10})/(-3m^2n^5))^{-1} ?

The solution to ((9m^4n^{10})/(-3m^2n^5))^{-1} is -1/(3m^2n^5)

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simplify ((9m^4n^{10})/(-3m^2n^5))^{-1}

simplify

(\frac{9 m ^{4} n ^{10}}{- 3 m ^{2} n ^{5}})^{- 1}

- \frac{1}{3 m ^{2} n ^{5}}

Solution steps

(\frac{9 m ^{4} n ^{10}}{- 3 m ^{2} n ^{5}})^{- 1}

Apply exponent rule:

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

(\frac{9 m ^{4} n ^{10}}{- 3 m ^{2} n ^{5}})^{- 1} = \frac{1}{\frac{9 m ^{4} n ^{10}}{- 3 m ^{2} n ^{5}}}

= \frac{1}{\frac{9 m ^{4} n ^{10}}{- 3 m ^{2} n ^{5}}}

Apply the fraction rule:

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

= \frac{1}{- \frac{9 m ^{4} n ^{10}}{3 m ^{2} n ^{5}}}

Apply the fraction rule:

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

= - \frac{1}{\frac{9 m ^{4} n ^{10}}{3 m ^{2} n ^{5}}}

Apply the fraction rule:

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

\frac{1}{\frac{9 m ^{4} n ^{10}}{3 m ^{2} n ^{5}}} = \frac{3 m ^{2} n ^{5}}{9 m ^{4} n ^{10}}

= - \frac{3 m ^{2} n ^{5}}{9 m ^{4} n ^{10}}

Cancel the common factor:

3

= \frac{m ^{2} n ^{5}}{3 m ^{4} n ^{10}}

Apply exponent rule:

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

\frac{m ^{2}}{m ^{4}} = \frac{1}{m ^{4 - 2}}

= \frac{n ^{5}}{3 n ^{10} m ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

= \frac{n ^{5}}{3 m ^{2} n ^{10}}

Apply exponent rule:

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

\frac{n ^{5}}{n ^{10}} = \frac{1}{n ^{10 - 5}}

= \frac{1}{3 m ^{2} n ^{10 - 5}}

Subtract the numbers:

10 - 5 = 5

= - \frac{1}{3 m ^{2} n ^{5}}

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\frac{( x ^{2} ) ^{- 5}}{( y ^{- 3} ) ^{- 5}}

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What is ((9m^4n^{10})/(-3m^2n^5))^{-1} ?
The solution to ((9m^4n^{10})/(-3m^2n^5))^{-1} is -1/(3m^2n^5)