# How do you simplify sqrtx^3 timesroot3(x^2) and write it in exponential form?

May 1, 2016

${x}^{\frac{13}{6}}$ assuming $x \ge 0$

#### Explanation:

If $x \ge 0$ then ${\left({x}^{a}\right)}^{b} = {x}^{a b}$

and ${x}^{a} \times {x}^{b} = {x}^{a + b}$

Another way of writing $\sqrt[n]{x}$ is ${x}^{\frac{1}{n}}$

So:

${\sqrt{x}}^{3} \times \sqrt[3]{{x}^{2}}$

$= {\left({x}^{\frac{1}{2}}\right)}^{3} \times {\left({x}^{2}\right)}^{\frac{1}{3}}$

$= {x}^{\frac{1}{2} \cdot 3} \times {x}^{2 \cdot \frac{1}{3}}$

$= {x}^{\frac{3}{2}} \times {x}^{\frac{2}{3}}$

$= {x}^{\frac{3}{2} + \frac{2}{3}}$

$= {x}^{\frac{9}{6} + \frac{4}{6}}$

$= {x}^{\frac{13}{6}}$