SOLUTION: (8+x)^-3=64

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Question 894415: (8+x)^-3=64
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x%2B8%29%5E3=64
%28x%2B8%29%5E3=1%2F%288%2A8%29
%28x%2B8%29%5E3=1%2F%282%5E6%29
%28x%2B8%29%5E3=%281%2F2%29%5E6
%28%28x%2B8%29%5E3%29%5E%281%2F3%29=%28%281%2F2%29%5E6%29%5E%281%2F3%29, so a law of exponents can be used
%28x%2B8%29%5E%281%29=%281%2F2%29%5E2
x%2B8=1%2F4
x=1%2F4-8
x=1%2F4-32%2F4
x=-31%2F4

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

(8+x)^-3=64


%288+%2B+x%29%5E-+3+=+64

%288+%2B+x%29%5E-+3+=+4%5E3

%288+%2B+x%29%5E%28-+3+%2A+%28-+1%2F3%29%29+=+%284%5E3%29%5E%28-+1%2F3%29 ------ Raising each side to the -+1%2F3 power

8+%2B+x+=+4%5E%28-+1%29

8+%2B+x+=+1%2F4

32 + 4x = 1 ------- Multiplying by LCD, 4

4x = 1 – 32

highlight_green%28highlight_green%28x+=+-+31%2F4%29%29

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