I don't know how to show roots on a computer, but it is one radical (the top being the third root) divided by the bottom radical (w/o a root) and both are inside a bigger radical (which would be the 5th root). I tried starting with making the third root into an exponent 1/3 and multiplying the top, then squaring both radicals to get rid of the radicals, but I am still left with a radical and the 5th root around the answer. Would I then square it again? HELP!!
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You can show radicals as a fractional power ... for example...the third root of a would be shown as:
a^(1/3)
So your problem, I think, would be written as:
[ [(a^2)b]^(1/3) / (ab)^(1/2)]^(1/5)
Now you multiply exponents: eg. (x^2)^3 = x^6
[ [ a^(2/3)b^(1/3) ] / a^(1/2)b^(1/2) ]^(1/5)
You subtract exponents when you divide: eg. x^5 / x^2 = x^3
[ [a^(1/6)b^(-1/6)]^(1/5) now multiply exponents again
a^(1/30)b^(-1/30) = (a/b)^(1/30)
Answer is the 30th root of (a/b)
a^(1/3)
So your problem, I think, would be written as:
[ [(a^2)b]^(1/3) / (ab)^(1/2)]^(1/5)
Now you multiply exponents: eg. (x^2)^3 = x^6
[ [ a^(2/3)b^(1/3) ] / a^(1/2)b^(1/2) ]^(1/5)
You subtract exponents when you divide: eg. x^5 / x^2 = x^3
[ [a^(1/6)b^(-1/6)]^(1/5) now multiply exponents again
a^(1/30)b^(-1/30) = (a/b)^(1/30)
Answer is the 30th root of (a/b)