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!

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) (Show Source): You can put this solution on YOUR website!

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 and 2 as :

Replacing the radicals with their fractional exponent equivalent:

Now we use our rules for exponents to simplify:
Rule: Multiply when raising a power to a power
Rule: (a*b)^q = a^q*b*q
Rule: Power of a power
Rule: Subtract exp. when dividing

Rule: Negative exponents
Match the denominators in the exponents
Rule:

Rule:
So the answer is the 6th root of a/8, not the 5th root.
RELATED QUESTIONS
Quick question. 23-(x-7) Trying to understand how this is solved. I know the... (answered by josgarithmetic)

Quadratic equations: Find two possitive numbers that differ by 2 and have a producy of (answered by Earlsdon)

Hi thankyou so much for answering my question las time, I need a help again, don't worry... (answered by ikleyn)

Hi guys, this is a proofing type question. There are three parts - I don't know how to (answered by ikleyn)

Hi I have a question: ((3x-2)/(x+2))-(2/(x-2)) I know that the answer is 3/(x+2) (answered by mananth)

Hi, i don't really know what to do here. The linear operator A is called the... (answered by parmen)

Hi, Nick again. I have another question, this time regarding how to "Make t the subject... (answered by stanbon)

Find the real solutions, if any, of each system. {3m^2-2n^2= 9 {m^2-n^2= -1 The... (answered by longjonsilver)

What is the distribution of the weights of a sample of 1,300 cargo containers is... (answered by Solver92311)