Chapter 6.6, Problem 30PPS

To determine

Simplify the expression $x^{\frac{1}{3}}\cdot x^{\frac{2}{5}}$ .

Answer to Problem 30PPS

The simplified value of expression $x^{\frac{1}{3}}\cdot x^{\frac{2}{5}}$ is $x^{\frac{11}{15}}$ .

Explanation of Solution

Given information: The given expression is $x^{\frac{1}{3}}\cdot x^{\frac{2}{5}}$ .

Calculation: The given expression $x^{\frac{1}{3}}\cdot x^{\frac{2}{5}}$ can be simplified as,

  $\begin{array}{c}{x}^{\frac{1}{3}}\cdot x^{\frac{2}{5}}={\left(x\right)}^{\frac{1}{3}+\frac{2}{5}}\mathrm{......}\left(\text{Using }{\left(x\right)}^m\cdot {\left(x\right)}^n=x^{m+n}\right)\\ ={\left(x\right)}^{\frac{5+6}{15}}\\ =x^{\frac{11}{15}}\end{array}$