## Intermediate Algebra for College Students (7th Edition)

$\sqrt[4]{8}-10\sqrt[3]{4}$
Rationalize $\displaystyle \frac{20}{ \sqrt[3]{2}}$ $\displaystyle \frac{20}{ \sqrt[3]{2}}\color{red}{ \cdot\frac{ \sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}} }=\frac{20\sqrt[3]{2^{2}}}{\sqrt[3]{2^{3}}}=\frac{20\sqrt[3]{4}}{2}=10\sqrt[3]{4}$ $\displaystyle \sqrt[4]{8}-\frac{20}{ \sqrt[3]{2}}=\sqrt[4]{8}-10\sqrt[3]{4}$ $\sqrt[4]{8}=\sqrt[4\cdot 3]{8^{3}}=\sqrt[12]{512}$ $\sqrt[3]{4}=\sqrt[3\cdot 4]{4^{4}}=\sqrt[12]{256}\quad$ so there are no common terms and we can not simplify further.