# How do you simplify x^(3/7)/x^(1/3)?

Mar 24, 2017

${x}^{\frac{2}{21}}$

#### Explanation:

"If you are dividing and the bases are the same, subtract the indices."

Consider: ${x}^{8} / {x}^{3} = {x}^{8 - 3} = {x}^{5}$

In the same way:

$\frac{{x}^{\frac{3}{7}}}{{x}^{\frac{1}{3}}} = {x}^{\frac{3}{7} - \frac{1}{3}}$

Working with the fractions: find the LCD

$\frac{3}{7} - \frac{1}{3} = \frac{9 - 7}{21} = \frac{2}{21}$

${x}^{\frac{3}{7} - \frac{1}{3}} = {x}^{\frac{2}{21}}$

Mar 24, 2017

${x}^{\frac{2}{21}}$

#### Explanation:

We know, a = $\frac{1}{a} ^ - 1. S o , \frac{1}{x} ^ \left(\frac{1}{3}\right) = {x}^{- \frac{1}{3}}$

Thereby ${x}^{\frac{3}{7}} / {x}^{\frac{1}{3}} = {x}^{\frac{3}{7}} . {x}^{- \frac{1}{3}} = {x}^{\frac{3}{7} - \frac{1}{3}}$

$\Rightarrow {x}^{\frac{9 - 7}{21}} = {x}^{\frac{2}{21}}$