SOLUTION: I am asked to evaluate the expression: (125/216)^2/3 I am unsure on how to work this out. Can you please help me as I have other problems like this. Thank you so much for your tim

Algebra ->  Algebra  -> Expressions -> SOLUTION: I am asked to evaluate the expression: (125/216)^2/3 I am unsure on how to work this out. Can you please help me as I have other problems like this. Thank you so much for your tim      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 237960: I am asked to evaluate the expression: (125/216)^2/3
I am unsure on how to work this out. Can you please help me as I have other problems like this. Thank you so much for your time.
Very respectfully,
Misty
Found 3 solutions by Alan3354, scott8148, josmiceli:
Answer by Alan3354(21584) About Me  (Show Source):
You can put this solution on YOUR website!
(125/216)^2/3
----------
= %28%28125%2F216%29%5E%281%2F3%29%29%5E2
Take the cube roots first.
= %285%2F6%29%5E2
= 25/36

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
when you have a fractional exponent; think of the numerator (top) as a power, and the denominator (bottom) as a root

the 2/3 in the problem means "cuberoot, squared"

the cuberoot of 125 is 5; 5 squared is 25

the cuberoot of 216 is 6; 6 squared is 36

(125/216)^2/3 = 25/36

Answer by josmiceli(6784) About Me  (Show Source):
You can put this solution on YOUR website!
%28125%2F216%29%5E%282%2F3%29
What you have to do is try to express 125 and 216 in
terms of cubes. You can use a calculator or just play with numbersd
until you hit on the answer. Rewrite the equation like this:
%28%28125%2F216%29%5E%281%2F3%29%29%5E2
%28%285%5E3%2F6%5E3%29%5E%281%2F3%29%29%5E2%29
Rewrite again
%28%28%285%2F6%29%5E3%29%5E%281%2F3%29%29%5E2
Rewrite again
%28%285%2F6%29%5E%283%2F3%29%29%5E2
%285%2F6%29%5E2
25%2F36 answer
check answer:
%28125%2F216%29%5E%282%2F3%29+=+%285%2F6%29%5E2
Take the square root of both sides
%28125%2F216%29%5E%281%2F3%29+=+5%2F6
Cube both sides
125%2F216+=+125%2F216
OK