# How do you simplify 70^(1/3)/14^(1/3)?

Jun 16, 2017

## $\sqrt[3]{5} = 1.70997594668$

#### Explanation:

If both the denominator and numerator are raised to the same exponent, it can be rewritten outside of the fraction because it will get distributed anyways.
[It may not make sense right now, so see numbers below.]

## ${70}^{\frac{1}{3}} / {14}^{\frac{1}{3}}$ = ${\left(\frac{70}{14}\right)}^{\frac{1}{3}}$

A fractional exponent can be rewritten as a root and exponent.
denominator $\to$ root
numerator $\to$ exponent

[It may not make sense right now, so see numbers below.]

## ${\left(\frac{70}{14}\right)}^{\frac{1}{3}}$ = ${\left(\sqrt[3]{\frac{70}{14}}\right)}^{1}$

Simplify $\left(\frac{70}{14}\right)$.

## ${\left(\sqrt[3]{\frac{70}{14}}\right)}^{1} = {\left(\sqrt[3]{5}\right)}^{1}$

Anything to the first power is itself.