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i don't know how to do this. if somebody could walk me through it, that would be great!

(8/125)^-1/3!

 Sep 2, 2020
edited by Guest  Sep 2, 2020
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1. Apply the exponent rule turning the expression into 1/(8/125)^(-1/3).

 

2. The denominator (8/125)^(1/3) can be rewritten as (8^(1/3))/(125^(1/3)).

 

3. Factor 8^(1/3) into (2^3)^(1/3) which equals 2^(3*1/3) which equals 2. Now let's find the denominator. Factor 125^(1/3) into (5^3)^(1/3) which equals 5^(3*1/3) which equals 5.

 

4. We can't forget about that 1 at the very top of the fraction from the beginning, so we have to simplify 1/2/5. (1)/(2/5)=(1)(5/2)=5/2 or 2 1/2.

 

Answer: 5/2 or 2 1/2 smiley

Edit: I messed up some signs... YIKES... but they're good now!

 Sep 2, 2020
edited by joliel3  Sep 2, 2020
edited by joliel3  Sep 2, 2020

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