SOLUTION: What is -64 raised to the 2/3?

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Question 189879: What is -64 raised to the 2/3?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given expression.


%28root%283%2C-64%29%29%5E2 Convert to radical notation


%28root%283%2C%28-4%29%5E3%29%29%5E2 Rewrite -64 as %28-4%29%5E3


%28-4%29%5E2 Take the cube root of %28-4%29%5E3 to get -4


16 Square -4 to get 16


So

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!



A fractional exponent means raise the number to the power of the numerator and take the root indicated by the denominator. Here, you can either square -64 and take the cube root of the result, or you can take the cube root of -64 and square the result. The order doesn't matter except that the second way is computationally easier if you are doing it in your head. I did it in my head and got 16. Check it out on the calculator.

John