# How do you write root3(10)^7 in rational exponent notation?

Apr 9, 2017

${10}^{\frac{7}{3}}$

#### Explanation:

$\sqrt[3]{10}$ is ${10}^{\frac{1}{3}}$ as the power on $\sqrt[3]{10}$ is 1.

Hence, ${\sqrt[3]{10}}^{7}$ would be ${10}^{\frac{7}{3}}$.

Apr 9, 2017

${\sqrt[3]{10}}^{7} = {10}^{\frac{7}{3}}$

#### Explanation:

Given: ${\sqrt[3]{10}}^{7}$

Can also be stated as the cube root of 10 to the power of seven.

${\sqrt[3]{10}}^{7} = {\left({10}^{7}\right)}^{\frac{1}{3}} = {10}^{\frac{7}{3}}$