What is ((m^5n^5)^{1/6})/(3(mn)^{-1/6)} ?

The solution to ((m^5n^5)^{1/6})/(3(mn)^{-1/6)} is (mn)/3

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simplify ((m^5n^5)^{1/6})/(3(mn)^{-1/6)}

simplify

\frac{( m ^{5} n ^{5} ) ^{\frac{1}{6}}}{3 ( mn ) ^{- \frac{1}{6}}}

\frac{mn}{3}

Solution steps

\frac{( m ^{5} n ^{5} ) ^{\frac{1}{6}}}{3 ( mn ) ^{- \frac{1}{6}}}

Simplify

(m^{5} n^{5})^{\frac{1}{6}} : m^{\frac{5}{6}} n^{\frac{5}{6}}

= \frac{m ^{\frac{5}{6}} n ^{\frac{5}{6}}}{3 ( mn ) ^{- \frac{1}{6}}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(mn)^{- \frac{1}{6}} = m^{- \frac{1}{6}} n^{- \frac{1}{6}}

= \frac{m ^{\frac{5}{6}} n ^{\frac{5}{6}}}{3 m ^{- \frac{1}{6}} n ^{- \frac{1}{6}}}

Simplify

\frac{m ^{\frac{5}{6}}}{m ^{- \frac{1}{6}}} : m

= \frac{m n ^{\frac{5}{6}}}{3 n ^{- \frac{1}{6}}}

Simplify

\frac{n ^{\frac{5}{6}}}{n ^{- \frac{1}{6}}} : n

= \frac{mn}{3}

(24 c)^{\frac{2}{3}}

5 x^{2} + 5 x + 9 = 0

x^{2} + 11 x y - 26 y^{2}

\frac{m}{26} = - \frac{1}{2}

8 m^{2} - 4 mn

What is ((m^5n^5)^{1/6})/(3(mn)^{-1/6)} ?
The solution to ((m^5n^5)^{1/6})/(3(mn)^{-1/6)} is (mn)/3