SOLUTION: 27 ^ -2/3 ----------- - 27 ^ -1/3 This is what I have done: I moved the bottom expression to the top. Then take the LCD of 6, which changes the expressions to 27 ^ -4/6 + 2

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: 27 ^ -2/3 ----------- - 27 ^ -1/3 This is what I have done: I moved the bottom expression to the top. Then take the LCD of 6, which changes the expressions to 27 ^ -4/6 + 2      Log On


   

Question 876431: 27 ^ -2/3
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27 ^ -1/3
This is what I have done:
I moved the bottom expression to the top. Then take the LCD of 6, which changes the expressions to 27 ^ -4/6 + 27 ^ -2/6. Add the two expressions which gives me 27 ^ -6/6. Then to eliminate negative exponent, expression is put under 1.....like this
1
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27 ^ 6/6
Final answer is
1
-----------
27
I'm not sure, please help me
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The exponents are -2/3 and -1/3

Subtract them to get -2/3 - (-1/3) = -2/3 + 1/3 = (-2+1)/3 = -1/3

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So that tells us

\frac{27^{-2/3}}{27^{-1/3}} = 27^{-1/3}

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Now simplify 27%5E%28-1%2F3%29%5E%22%22 to get

27%5E%28-1%2F3%29%5E%22%22+=+1%2F%2827%5E%281%2F3%29%5E%22%22%29


27%5E%28-1%2F3%29%5E%22%22+=+1%2F%28root%283%2C27%29%29


27%5E%28-1%2F3%29%5E%22%22+=+1%2F%28root%283%2C3%5E3%29%29


27%5E%28-1%2F3%29%5E%22%22+=+1%2F3

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In the end,

\frac{27^{-2/3}}{27^{-1/3}} = \frac{1}{3}