SOLUTION: Evaluate: ((1/sqrt8)^(-2/3))-81^0.75

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Question 937581: Evaluate: ((1/sqrt8)^(-2/3))-81^0.75
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28%281%2Fsqrt%288%29%29%5E%28-2%2F3%29%29-81%5E0.75 ........since 0.75=75%2F100=3%2F4, we have

%281%2F%281%2F%28sqrt%288%29%29%5E%282%2F3%29%29%29-81%5E%283%2F4%29

sqrt%288%29%5E%282%2F3%29-81%5E%283%2F4%29

root%283%2C%28sqrt%288%29%29%5E2%29-root%284%2C81%5E3%29 .......since 81%5E3=%289%5E2%29%5E3=9%5E6=%283%5E2%29%5E6=3%5E12, we have

root%283%2C8%29-root%284%2C3%5E12%29 .........since 3%5E12=3%5E3%2A3%5E3%2A3%5E3%2A3%5E3=%283%5E3%29%5E4, we have

root%283%2C3%5E3%29-root%284%2C%283%5E3%29%5E4%29

3-3%5E3

3-9

-6


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate: ((1/sqrt8)^(-2/3))-81^0.75
Evaluate: %281%2Fsqrt%288%29%29%5E%28-+2%2F3%29+-+81%5E0.75

highlight%28highlight%28%28sqrt%288%29%29%5E%282%2F3%29+-+%2881%29%5E%283%2F4%29%29%29

%288%5E%281%2F2%29%29%5E%282%2F3%29+-+%28root%284%2C81%29%29%5E3 

highlight%28highlight%288%5E%28%281%2F2%29+%2A+%282%2F3%29%29+-+3%5E3%29%29



highlight%28highlight%288%5E%281%2F3%29+-+3%5E3%29%29

root%283%2C+8%29+-+3%5E3_________2+-+27________highlight_green%28-+25%29

You can do the check!! 

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