SOLUTION: If x greater than 1 and square root x over x^3 = x^m, what is the value of m?

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Question 794181: If x greater than 1 and square root x over x^3 = x^m, what is the value of m?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Use the property
(1) %28a%5Ej%29%2F%28a%5Ek%29+=+a%5E%28j-k%29
and for your example j = 1/2 and k = 3 to get
(2) %28a%5E%281%2F2%29%29%2F%28a%5E3%29+=+a%5E%281%2F2+-+3%29 or
(3) %28a%5E%281%2F2%29%29%2F%28a%5E3%29+=+a%5E%28-5%2F2%29 from which we see that you get
(4) m = -5/2
Answer: m = -5/2