Answer
$4x^{\frac{4}{15}}$
Work Step by Step
We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression:
$\frac{24x^{\frac{3}{5}}}{6x^{\frac{1}{3}}}$
$=\frac{24}{6}\times\frac{x^{\frac{3}{5}}}{x^{\frac{1}{3}}}$
$=4\times x^{\frac{3}{5}-(\frac{1}{3})}$
$=4\times x^{\frac{3(3)-1(5)}{15}}$
$=4\times x^{\frac{9-5}{15}}$
$=4\times x^{\frac{4}{15}}$
$=4x^{\frac{4}{15}}$
