Question

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

Answer 1

`16n^20*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 `(4n)^2` becomes `16n^2`.

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

Next, you would simplify the denominator. First, multiply the like terms. `n^-1*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 `16n^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 `16n^11*1/512*n^9`

Now you can just combine the n's and you get `16n^20*1/512`.

Hope this helps! :)