SOLUTION: Hi, I have a question. (2(cubedroot of a^2)) / (squareroot of 8a) = I know that the answer is: (fifthroot of (a/8)) I just don't understand how to get this?? Thanks!

Algebra ->  Square-cubic-other-roots -> SOLUTION: Hi, I have a question. (2(cubedroot of a^2)) / (squareroot of 8a) = I know that the answer is: (fifthroot of (a/8)) I just don't understand how to get this?? Thanks!      Log On


   

Question 609668: Hi, I have a question.
(2(cubedroot of a^2)) / (squareroot of 8a) =
I know that the answer is:
(fifthroot of (a/8))
I just don't understand how to get this??
Thanks!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282%28root%283%2C+a%5E2%29%29%29%2F%28sqrt%288a%29%29
Keys to this problem are:
  • Understanding that roots/radicals can be replaced with fractional exponents.
  • 8 is a power of 2.
First let's rewrite 8 as 2%5E3 and 2 as 2%5E1:
%282%5E1%2A%28root%283%2C+a%5E2%29%29%29%2F%28sqrt%282%5E3%2Aa%29%29
Replacing the radicals with their fractional exponent equivalent:
%282%5E1%2A%28a%5E2%29%5E%281%2F3%29%29%2F%282%5E3%2Aa%29%5E%281%2F2%29
Now we use our rules for exponents to simplify:
%282%5E1%2Aa%5E%282%2F3%29%29%2F%282%5E3%2Aa%29%5E%281%2F2%29 Rule: Multiply when raising a power to a power
%282%5E1%2Aa%5E%282%2F3%29%29%2F%28%282%5E3%29%5E%281%2F2%29%2Aa%5E%281%2F2%29%29 Rule: (a*b)^q = a^q*b*q
%282%5E1%2Aa%5E%282%2F3%29%29%2F%282%5E%283%2F2%29%2Aa%5E%281%2F2%29%29 Rule: Power of a power
2%5E%281-%283%2F2%29%29%2Aa%5E%28%282%2F3%29-%281%2F2%29%29 Rule: Subtract exp. when dividing
2%5E%28-%281%2F2%29%29%2Aa%5E%281%2F6%29
a%5E%281%2F6%29%2F2%5E%281%2F2%29 Rule: Negative exponents
a%5E%281%2F6%29%2F2%5E%283%2F6%29 Match the denominators in the exponents
root%286%2C+a%29%2Froot%286%2C+2%5E3%29 Rule: a%5E%28t%2Fu%29+=+root%28u%2C+a%5Et%29
root%286%2C+a%29%2Froot%286%2C+8%29
root%286%2C+a%2F8%29 Rule: root%28a%2C+p%29%2Froot%28a%2C+q%29+=+root%28a%2C+p%2Fq%29
So the answer is the 6th root of a/8, not the 5th root.