# How do you simplify this expression 4c^4sqrt(64c^9 x^6)?

Mar 24, 2018

$\implies 32 {c}^{\frac{17}{2}} {x}^{3}$

#### Explanation:

$4 {c}^{4} \sqrt{64 {c}^{9} {x}^{6}}$

Taking the square root is equivalent to raising to the $\frac{1}{2}$ power.

$\implies 4 {c}^{4} {\left(64 {c}^{9} {x}^{6}\right)}^{\frac{1}{2}}$

$\implies 4 {c}^{4} \left(8 {c}^{\frac{9}{2}} {x}^{3}\right)$

Now we distribute the $4 {c}^{4}$ into the quantity we took the square root of.

$\implies 32 {c}^{\left(4 + \frac{9}{2}\right)} {x}^{3}$

$\implies 32 {c}^{\frac{17}{2}} {x}^{3}$