# How do you write root8(15)^3 in rational exponent notation?

Oct 5, 2016

${\sqrt[8]{15}}^{3} = {15}^{\frac{3}{8}}$

The root becomes the denominator and the index becomes the numerator

#### Explanation:

"Rational" means in the form of a fraction. $\frac{a}{b} \text{ } b \ne 0$

Recall: one of the laws of indices: $\sqrt[q]{{x}^{p}} = {x}^{\frac{p}{q}}$

The root becomes the denominator and the index becomes the numerator

Apply the law given above.

${\sqrt[8]{15}}^{3} = {15}^{\frac{3}{8}}$

The root becomes the denominator and the index becomes the numerator