SOLUTION: Evaluate: (-1)^2/3 In general, how can I evaluate when the base is negative and the exponent is a fraction?

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Question 1179387: Evaluate: (-1)^2/3
In general, how can I evaluate when the base is negative and the exponent is a fraction?
Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!
.

In this problem, you can move any of the two ways.


Way 1 

Take  first  (-1)^(1/3) = root%283%2C-1%29 = -1.


      Then square is  %28-1%29%5E2 = 1.      ANSWER


      So, I calculated  (-1)^(2/3)   according this formula  (-1)^(2/3) = ((-1)^(1/3))^2.



Way 2 

Take  first  (-1)^2 = 1.


      Then take the degree  (1/3)  of it  1^(1/3) = 1.      ANSWER


      So, this time I calculated  (-1)^(2/3)   according this formula  (-1)^(2/3) = ((-1)^2)^(1/3).


Both ways lead you to the same result.


The meaning is this: 

    To calculate  a^(m/n),  you can raise  "a"  to degree  m  first,  and then take the root of the degree  n.


    Or you can do it differently:  To calculate  a^(m/n),  you can take the degree  "n"  root of  "a" 

    and then raise it to degree "m".


    Both ways lead to the same answer, if you make all intermediate calculations correctly.

Do you understand everything in my explanations ?

If you still have questions, DO NOT HESITATE to ask them.


Happy learning (!)