What is ((m^{-3/2})^{2/3})/((m^{-2))} ?

The solution to ((m^{-3/2})^{2/3})/((m^{-2))} is m

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simplify ((m^{-3/2})^{2/3})/((m^{-2))}

simplify

\frac{( m ^{- \frac{3}{2}} ) ^{\frac{2}{3}}}{( m ^{- 2} )}

m

Solution steps

\frac{( m ^{- \frac{3}{2}} ) ^{\frac{2}{3}}}{m ^{- 2}}

Simplify

(m^{- \frac{3}{2}})^{\frac{2}{3}} : \frac{1}{m}

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

Apply the fraction rule:

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

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

Simplify

m m^{- 2} : \frac{1}{m}

= \frac{1}{\frac{1}{m}}

Apply the fraction rule:

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

= \frac{m}{1}

Apply the fraction rule:

\frac{a}{1} = a

= m

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What is ((m^{-3/2})^{2/3})/((m^{-2))} ?
The solution to ((m^{-3/2})^{2/3})/((m^{-2))} is m