Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Problem Set 11.3 - Page 489: 74

$2n$

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression: $\frac{16n^{\frac{1}{3}}}{8n^{-\frac{2}{3}}}$ $=\frac{16}{8}\times\frac{n^{\frac{1}{3}}}{n^{-\frac{2}{3}}}$ $=2\times n^{\frac{1}{3}+(\frac{2}{3})}$ $=2\times n^{\frac{1(1)+1(2)}{3}}$ $=2\times n^{\frac{1+2}{3}}$ $=2\times n^{\frac{3}{3}}$ $=2\times n$ $=2n$