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(256/x^12)^ -3/4
(256/x^12)^ -3/4 is the same as (256)^(-3/4)/(x^12)^(-3/4)
Negative exponents need to be moved up or down to make them positive so this expression is really the same as (x^12)^(3/4)/(256)^(3/4). the 3/4 power is the same as taking the 4th root and then cubing the answer or cubing the number and then taking the 4th root. For example 8^(2/3) is the same as 8 raised to the 2nd power (64) then taking the 3rd root of 64 = 4 OR take the 3rd root of 8 = 2 and the squaring 2 getting 4. See you get the same answer either way. So onto your problem:
(x^12)^(3/4)= x^9 [multiply powers to powers] and (256)^(3/4) I will take the 4th root of 256 = 4 and then cube 4 getting 64. Thus your answer is x^9/64.
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Sherry Wallin
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