# How do you simplify (125x)^(2/3)?

Mar 22, 2018

${\left(125 x\right)}^{\frac{2}{3}}$ = $\left({125}^{\frac{2}{3}} \cdot {x}^{\frac{2}{3}}\right)$ = $\left({5}^{2} \cdot {x}^{\frac{2}{3}}\right)$ = $\left(25 \cdot {x}^{\frac{2}{3}}\right)$

#### Explanation:

${\left(125 x\right)}^{\frac{2}{3}}$
says:
( remember that ${\left(125 x\right)}^{\frac{2}{3}}$ = ${\left({\left(125 x\right)}^{2}\right)}^{\frac{1}{3}}$ )
125x multiplied by itself twice(because of the 2 exponent) (i'll say that in math: (125x)^(2) ) then all that multiplied by itself 1/3 times (aka taking the cube root of that)
${\left(125 x\right)}^{2} = 15625 \cdot {x}^{2}$
now for cube root:
${\left(15625 \cdot {x}^{2}\right)}^{\frac{1}{3}}$
$\left({15625}^{\frac{2}{3}} \cdot {x}^{\frac{2}{3}}\right)$
$25 \cdot {x}^{\frac{2}{3}}$
you could've also instead of squaring first, then taking the cube root,
you could've of cube rooted first, then squared,
or:
you could've done both at the same time: (which is what you see in the awnser up top)