SOLUTION: Third root of a^8 / (√a)^3 = a^x , where a > 1 In the equation above, what is the value of x?

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Question 1105183: Third root of a^8 / (√a)^3 = a^x , where a > 1
In the equation above, what is the value of x?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Third root of a^8 / (√a)^3 = a^x , where a > 1
In the equation above, what is the value of x?
%28a%5E8%2F%28%28sqrt%28a%29%29%5E3%29%29%5E%281%2F3%29 = a%5Ex
multiply the inside exponents by the outside exponent, 1/3
%28a%5E%288%2F3%29%2F%28%28sqrt%28a%29%29%5E1%29%29 = a%5Ex; the top exponent is 8/3
the denominator can be written
%28a%5E%288%2F3%29%2Fa%5E%281%2F2%29%29 = a%5Ex
:
a%5E%288%2F3-1%2F2%29 = a%5Ex; that's 8%2F3-1%2F2
a%5E%2816%2F6-3%2F6%29 = a%5Ex, that's 16%2F6-3%2F6
a%5E%2813%2F6%29 = a%5Ex, that's 13%2F6
therefore
x = 13%2F6