# How do you simplify (x^(2/9))^(3/8)?

Oct 23, 2016

${x}^{\frac{1}{12}} \text{ "or" } \sqrt[12]{x}$

#### Explanation:

Recall: one of the laws of indices:

${\left({x}^{m}\right)}^{n} = {x}^{m \times n}$

Raising a power to a power, multiply the indices.

${\left({x}^{\frac{2}{9}}\right)}^{\frac{3}{8}} = {x}^{\frac{2 \times 3}{9 \times 8}} \text{ } \leftarrow \frac{\cancel{2} \times \cancel{3}}{{\cancel{9}}^{3} \times {\cancel{8}}^{4}} = \frac{1}{12}$

=${x}^{\frac{1}{12}}$

This can also be written as $\sqrt[12]{x}$