SOLUTION: simplify or put in standard terms: (8/27)^-(1/3)

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Question 144132: simplify or put in standard terms: (8/27)^-(1/3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%288%2F27%29%5E%28-1%2F3%29 Start with the given expression


%2827%2F8%29%5E%281%2F3%29 Reciprocate the fraction. Remember, %28a%2Fb%29%5E%28-c%29=%28b%2Fa%29%5Ec


%2827%29%5E%281%2F3%29%2F%288%29%5E%281%2F3%29 Distribute the exponent


root%283%2C27%29%2Froot%283%2C8%29 Rewrite the rational expression into radical notation


3%2Froot%283%2C8%29 Take the cube root of 27 to get 3


3%2F2 Take the cube root of 8 to get 2



So %288%2F27%29%5E%28-1%2F3%29=3%2F2