What is ((n^{2/3})/(m^{4/3)})^{1/2} ?

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

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simplify ((n^{2/3})/(m^{4/3)})^{1/2}

simplify

(\frac{n ^{\frac{2}{3}}}{m ^{\frac{4}{3}}})^{\frac{1}{2}}

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

Solution steps

(\frac{n ^{\frac{2}{3}}}{m ^{\frac{4}{3}}})^{\frac{1}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( n ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{( m ^{\frac{4}{3}} ) ^{\frac{1}{2}}}

Simplify

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

= \frac{n ^{\frac{1}{3}}}{( m ^{\frac{4}{3}} ) ^{\frac{1}{2}}}

Simplify

(m^{\frac{4}{3}})^{\frac{1}{2}} : m^{\frac{2}{3}}

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

Combine same powers :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = (\frac{x ^{a}}{y ^{b}})^{\frac{1}{m}}

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

\frac{5}{16 x ^{3} y ^{2}} + \frac{5}{6 x ^{2} y}

(2 a^{2} b^{3} c)^{4}

(\frac{5}{8})^{- 2}

117

25 + 4

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