Chapter A.10, Problem 72AYU

To determine

To find: Simplify the expression $x^{\frac{2}{3}}{x}^{\frac{1}{2}}{x}^{-\frac{1}{4}}$.

Answer to Problem 72AYU

The simplest form of $x^{\frac{2}{3}}{x}^{\frac{1}{2}}{x}^{-\frac{1}{4}}$ is $x^{\frac{11}{12}}$.

Explanation of Solution

Given:

It is asked to simplify the expression $x^{\frac{2}{3}}{x}^{\frac{1}{2}}{x}^{-\frac{1}{4}}$.

Calculation:

Consider $x^{\frac{2}{3}}{x}^{\frac{1}{2}}{x}^{-\frac{1}{4}}$.

$x^{\frac{2}{3}}{x}^{\frac{1}{2}}{x}^{-\frac{1}{4}}=x^{\frac{2}{3}+\frac{1}{2}-\frac{1}{4}}=x^{\frac{8+6-3}{12}}=x^{\frac{11}{12}}$