# How do you simplify \frac { ( 4n ) ^ { 2} n ^ { 3} } { n ^ { - 1} n ^ { - 5} } ( 8n ^ { - 3} ) ^ { - 3}?

Jan 3, 2017

$16 {n}^{20} \cdot \frac{1}{512}$

#### Explanation:

So first, you would simplify the numerator of this. You would take the square outside of the parenthesis and distribute to all the numbers inside of it. so the ${\left(4 n\right)}^{2}$ becomes $16 {n}^{2}$.

You would then multiply the like terms (n's) together and that would be $16 {n}^{5}$ since you add the exponents.

Next, you would simplify the denominator. First, multiply the like terms. ${n}^{-} 1 \cdot {n}^{-} 5$ becomes ${n}^{-} 6$.

Since a negative power is the reciprocal of the number (for example, ${5}^{-} 1$ is 1/5 and ${5}^{-} 2$ is 1/25) then you would just multiply the ${n}^{6}$ to the numerator.

So the numerator becomes $16 {n}^{11}$

Then, you would distribute the second value. The negatives in the n's cancel and you would just make the n ${n}^{9}$.You then simplify ${8}^{3}$ which is 512 and then make it its reciprocal. what we have now is $16 {n}^{11} \cdot \frac{1}{512} \cdot {n}^{9}$

Now you can just combine the n's and you get $16 {n}^{20} \cdot \frac{1}{512}$.

Hope this helps! :)