Question

How do you simplify `((-15(ab)^2)/(5a^2b))^5`?

Answer 1

`(-3b)^5` or `-243b^5`

Explanation:

So we have

`((-15(ab)^2)/(5a^2b))^5`

First let's take that first square in the first term, since it's a multiplication the exponent goes to both numbers.

`((-15a^2b^2)/(5a^2b))^5`

Now we can get rid of any letters that show up equally in top and bottom, we have 2 `a`s on top and 2 in the bottom so they both go, but we only 1 `b` in the bottom and two on the top, so one of the `b`s on the top will remain.

`((-15b)/5)^5`

Now, we simplify the actual numbers, we know `15 = 3*5` so it's just a matter of factorizing and discarding equal factors on top and bottom.

`(-3b)^5`

Which is easy to compute if you so wish, the letter just gets the exponent, the minus sign continues to be a minus because `(-1)*(-1)^2*(-1)^2 = (-1)*1*1=-1`, which only leaves us to deal with the `3`, but since `3^5 = 3*(3)^2*(3)^2=3*9*9=3*81`, we only need to do one multiplication that isn't tabled.

`3*81 = 3*80 + 3*1 = 243`, so the final expression is

`(-3b)^5` or `-243b^5`