Fractional Exponents and Fractions

Question

When dealing with fractional exponents like in the question below, how do you combine them so the two "n's" in the first fraction become one? ((how do i combine $4/3$ with $1/3$)) The aim is to end up with only one 'n' in that fraction. Same goes for the 'm'. \begin{align*} & \frac{2^{\frac{1}{3}}mn^{\frac{4}{3}}}{5^{\frac{1}{3}}m^{\frac{1}{6}}n^{\frac{1}{3}}} \div \frac{n}{2m^{\frac{1}{6}}5^{\frac{1}{3}}}\\ & = \frac{2^{\frac{1}{3}}mn^{\frac{4}{3}}}{5^{\frac{1}{3}}m^{\frac{1}{6}}n^{\frac{1}{3}}} \cdot \frac{2m^{\frac{1}{6}}5^{\frac{1}{3}}}{n}\\ & = \end{align*}

Answer 1

As far as I can see this is what your term looks like:

$\frac{2^{\frac{1}{3}}m n^{\frac{4}{3}}}{5^{\frac{1}{3}}m^{\frac{1}{6}}n^{\frac{1}{3}}} \cdot \frac{2m^{\frac{1}{6}}5^{\frac{1}{3}}}{n}$

$=\frac{2^{\frac{1}{3}}m n^{\frac{4}{3}}}{n^{\frac{1}{3}}}\cdot \frac{2}{n}$

$=\frac{2^{\frac{1}{3}}m n^{\frac{4}{3}}}{n^{\frac{1}{3}}} \cdot \frac{2^{\frac{3}{3}}}{n^{\frac{3}{3}}}$

$=\frac{2^{\frac{4}{3}}m n^{\frac{4}{3}}}{n^{\frac{4}{3}}}$

$=\sqrt[3]{2^4}\cdot m$