SOLUTION: {{{64^(5/6)}}} it needs to be a negative (5/6) but it will not let me include that.

Algebra ->  Square-cubic-other-roots -> SOLUTION: {{{64^(5/6)}}} it needs to be a negative (5/6) but it will not let me include that.      Log On


   

Question 15149: 64%5E%285%2F6%29 it needs to be a negative (5/6) but it will not let me include that.
Answer by wgunther(43) About Me  (Show Source):
You can put this solution on YOUR website!
In order to answer 64%5E%28-5%2F6%29 you have to understand a few properties of exponents.
a%5E%28-b%29+=+1%2Fa%5Eb
a%5Eb%2Aa%5Ed+=+a%5E%28b%2Bd%29
%28a%5Eb%29%5Ec=a%5E%28bc%29
Those rules also apply to fracial exponents. There are two parts to a fractional exponent: the numberator of the exponent, which is the power index, and the denominator of the exponent with the root index. Therefore, a%5E%281%2F2%29+=+sqrt%28a%29 and so on.
To your problem,
64%5E%28-5%2F6%29
First handle the negative exponent. As shown in one of the properties I illustrated, a negative exponent just means "flip it".
%281%2F64%29%5E%285%2F6%29
Then, you can do the numerator first or the denominator. 64%5E5 is going to be pretty big so lets do the denominator first.
%28%281%2F64%29%5E%281%2F6%29%29%5E5
The 6th root of 64, meaning then number that satisfied x%5E6=64 is 2. Therefore you have:
%281%2F2%29%5E5
2^5 is 32, so the final answer is:
1%2F32