# How do you simplify (\frac { 2a ^ { 2} \cdot 2a b ^ { 2} } { a ^ { 4} b ^ { 5} } ) ^ { 3}?

May 15, 2017

$\frac{64}{{a}^{3} {b}^{9}}$

#### Explanation:

$2 a \cdot 2 a {b}^{2} = 4 {a}^{3} {b}^{2}$ (To multiply two numbers with indices, add the powers)

Take away ${b}^{2}$ from the numerator AND the denominator.
(To divide numbers with indices, subtract the powers)

Take away ${a}^{3}$ from the numerator AND the denominator.

Then, cube the numerator AND the denominator

${4}^{3} = 64$
$a {\left({b}^{3}\right)}^{3} = {a}^{3} {b}^{9}$