# How do you simplify (sqrt(144x))^6?

Apr 2, 2018

${\left(\sqrt{144 x}\right)}^{6} = 2985984 {x}^{3}$

#### Explanation:

We can rewrite square roots as powers of $\frac{1}{2}$:
${\left(\sqrt{144 x}\right)}^{6} = {\left({\left(144 x\right)}^{\frac{1}{2}}\right)}^{6}$

Now we can use the following exponent rule:
${\left({a}^{n}\right)}^{m} = {a}^{m n}$

$\therefore {\left({\left(144 x\right)}^{\frac{1}{2}}\right)}^{6} = {\left(144 x\right)}^{\frac{6}{2}} = {\left(144 x\right)}^{3}$

Now we can use another exponent rule:
${\left(a b\right)}^{n} = {a}^{n} {b}^{n}$

$\therefore {\left(144 x\right)}^{3} = {144}^{3} \cdot {x}^{3} = 2985984 {x}^{3}$