## Intermediate Algebra (6th Edition)

$\sqrt[4] (x^{3})$
$\sqrt x\times\sqrt[4] x=x^{\frac{1}{2}}\times x^{\frac{1}{4}}$ We can use the product rule to simplify, which holds that $a^{m}\times a^{n}=a^{m+n}$ (where a is a real number, and m and n are positive integers). Therefore, $x^{\frac{1}{2}}\times x^{\frac{1}{4}}=x^{\frac{2}{4}+\frac{1}{4}}=x^{\frac{3}{4}}=\sqrt[4] (x^{3})$