SOLUTION: Please help me evaluate (-27/8)^4/3 Thanks in advance.

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Question 763775: Please help me evaluate (-27/8)^4/3
Thanks in advance.
Found 4 solutions by josgarithmetic, rothauserc, MathLover1, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Both the 27 and the 8 are cubes, so I suspect you did not write the expression that you want evaluated. I will evaluate exactly what you wrote:
%28%28-27%2F8%29%5E4%29%2F3, the neg. rational number to fourth power; and then divided by 3.


%28%283%5E12%29%2F%282%5E12%29%29%2F3

%283%5E11%29%2F%282%5E12%29
highlight%28177147%2F4096%29


Did you really mean, %28-27%2F8%29%5E%284%2F3%29 ?
Easier to do the cube root process first, and then do the exponentiation by 4.
%28%28%28-3%5E3%29%2F2%5E3%29%5E%281%2F3%29%29%5E4
%28-3%2F2%29%5E4
81%2F16

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we are asked to evaluate (-27/8)^4/3
(-27/8)^4/3 means take the cube root of -1 * (27*27*27*27) / (8*8*8*8)
notice that the cube root of (27*27*27) / (8*8*8) = 27/8, so we have
27/8 * cube root of -1 * 27/8, but 3^3 = 27 and 2^2 =8, so we have
(27*3) / (8*2) * cube root of -1
now the cube root of -1 is -1, so the final answer is
-81/16

Answer by MathLover1(20850) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me evaluate (-27/8)^4/3
Thanks in advance.

%28-+27%2F8%29%5E%284%2F3%29

%28root%283%2C+-+27%2F8%29%29%5E%284%29

%28-+3%2F2%29%5E4 ----- highlight_green%2881%2F16%29

You can do the check!!

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