Question 413833: -625^-1/4
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! I hope you posted the problem exactly as it was given to you because
and
are not the same thing!! Exponents apply only to whatever is directly in front of them. So in
the exponent applies only to the 625. In
the exponent applies to (-625)
So is the same as
If you have trouble with negative and/or fractional exponents I find it can be helpful to factor the exponent in a special way:- If the exponent is negative, then factor out -1.
- If the exponent is fractional and the numerator is not a 1, then factor out the numerator. For example, if the exponent was 3/4, then factor out the 3: 3*(1/4).
Factoring your exponent in this way...
Your exponent is negative wo we will factor out -1:
Your exponent is fractional but the numerator is 1 so we are finished factoring the exponent. Once factored, each factor of the exponent tells us an operation to perform:- The -1, as an exponent, tells us to find a reciprocal.
- The 1/4, as an exponent, tells us to find a 4th root.
And since multiplication is Commutative we can do these operations in any order we choose! Since a reciprocal of 625 will create a fraction and since fractions are usually harder to deal with than integers and since  (makingthe 4th root of 625 easy), I choose to do the reciprocal last:
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