What is ((9m^{1/2}*n^{3/2}))/((m^{-7)*n*(m^3*n)^{1/2})} ?

The solution to ((9m^{1/2}*n^{3/2}))/((m^{-7)*n*(m^3*n)^{1/2})} is 9m^6

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simplify ((9m^{1/2}n^{3/2}))/((m^{-7)n(m^3n)^{1/2})}

simplify

\frac{( 9 m ^{\frac{1}{2}} \cdot n ^{\frac{3}{2}} )}{( m ^{- 7} \cdot n \cdot ( m ^{3} \cdot n ) ^{\frac{1}{2}} )}

9 m^{6}

Solution steps

\frac{9 m ^{\frac{1}{2}} n ^{\frac{3}{2}}}{m ^{- 7} n ( m ^{3} n ) ^{\frac{1}{2}}}

Simplify

\frac{m ^{\frac{1}{2}}}{m ^{- 7}} : m^{\frac{15}{2}}

= \frac{9 m ^{\frac{15}{2}} n ^{\frac{3}{2}}}{n ( m ^{3} n ) ^{\frac{1}{2}}}

Simplify

\frac{n ^{\frac{3}{2}}}{n} : n^{\frac{1}{2}}

= \frac{9 m ^{\frac{15}{2}} n ^{\frac{1}{2}}}{( m ^{3} n ) ^{\frac{1}{2}}}

Simplify

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

= \frac{9 m ^{\frac{15}{2}} n ^{\frac{1}{2}}}{m ^{\frac{3}{2}} n ^{\frac{1}{2}}}

Simplify

\frac{m ^{\frac{15}{2}}}{m ^{\frac{3}{2}}} : m^{6}

= \frac{9 m ^{6} n ^{\frac{1}{2}}}{n ^{\frac{1}{2}}}

Cancel the common factor:

n^{\frac{1}{2}}

= 9 m^{6}

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(3 m^{2} + 5 n^{2})^{3}

What is ((9m^{1/2}*n^{3/2}))/((m^{-7)*n*(m^3*n)^{1/2})} ?
The solution to ((9m^{1/2}*n^{3/2}))/((m^{-7)*n*(m^3*n)^{1/2})} is 9m^6