# How do you simplify root3(125x^21y^24)?

##### 1 Answer
May 11, 2016

$\sqrt[3]{125 {x}^{21} {y}^{24}} = 5 {x}^{7} {y}^{8}$

#### Explanation:

Notice that ${\left(5 {x}^{7} {y}^{8}\right)}^{3} = {5}^{3} {\left({x}^{7}\right)}^{3} {\left({y}^{8}\right)}^{3} = 125 {x}^{21} {y}^{24}$

So $5 {x}^{7} {y}^{8}$ is a cube root of $125 {x}^{21} {y}^{24}$

Any Real number has a unique Real cube root, so for Real values of $x$ and $y$ and Real cube roots, we can deduce that this is the cube root we want.