SOLUTION: i have to simplify a question. it is (8a^4b)that whole thing times the exponet of (2/3) OVER (ab)with an exponet of (-1/3) please help! i cant have any negatives! Thank you sam

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: i have to simplify a question. it is (8a^4b)that whole thing times the exponet of (2/3) OVER (ab)with an exponet of (-1/3) please help! i cant have any negatives! Thank you sam      Log On


   

Question 292914: i have to simplify a question. it is (8a^4b)that whole thing times the exponet of (2/3) OVER (ab)with an exponet of (-1/3) please help! i cant have any negatives!
Thank you
samantha
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
(8a^4b)that whole thing times the exponent of (2/3) OVER (ab)with an exponent of (-1/3)
:
Assume the problem is:
%288a%5E4b%29%5E%282%2F3%29%2F%28ab%29%5E%28-1%2F3%29
The reciprocal will get rid of the neg exponent on denominator
%288a%5E4b%29%5E%282%2F3%29%2A%28ab%29%5E%281%2F3%29
:
remove the bracket, multiply the exponents
:

the exponents not showing up very well, they should be:
2%2F3%29, 8%2F3, 2%2F3, 1%2F3, 1%2F3
:
We know 8^(2/3) = 4
:
%284%2Aa%5E%288%2F3%29%2Ab%5E%282%2F3%29%2Aa%5E%281%2F3%29%2Ab%5E%281%2F3%29%29
:
Combine the exponents of like terms
;
%284%2Aa%5E%28%288%2F3%29%2B%281%2F3%29%29%2Ab%5E%28%282%2F3%29%2B%281%2F3%29%29%29 = %284%2Aa%5E%289%2F3%29%2Ab%5E%283%2F3%29%29%29 = %284%2Aa%5E3%2Ab%5E1%29%29 = %284%2Aa%5E3%2Ab%29