SOLUTION: how do you even begin solving this problem (16 to the -5 power) to the 1/20 power

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Question 395705: how do you even begin solving this problem
(16 to the -5 power) to the 1/20 power
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%2816%5E%28-5%29%29%5E%28%281%2F20%29%29
As often happens there are several ways this problem can be done. The most obvious first step is to use the rule for exponents when raising a power to a power. The rule is to multiply the exponents:
16%5E%28%28-5%29%2A%281%2F20%29%29
which simplifies as follows:
16%5E%28%28-5%29%2F20%29
16%5E%28%28-1%29%2F4%29
Next we try to simplify this expression even more. If you have trouble with negative and/or fractional exponents, I find it helpful to factor the exponent is a certain way:
  1. If the exponent is negative, then factor out -1.
  2. If the exponent is fractional and the numerator is not a 1, then factor out the numerator. For example, if the exponent was 2/3, then factor out the 2 as follows: 2*1/3.

After factoring the exponent in this way, look at the factors. Each one tells you one operation that will be done. And since multiplication is Commutative, these operations can be done in any order you choose!

Let's see how this works on your expression. First we factor the exponent:
16%5E%28%28-1%29%2A%281%2F4%29%29
Looking at the factors of the exponent, the -1 tells us that a reciprocal will be found. And the 1/4 tells us that a 4th root will be found. And the order we do them will not make any difference! So let's choose the order that seems the easiest. Normally a 4th root sounds difficult. But once you realize that 16 is 2%5E4 then the 4th root is quite easy. So we will start with that. And then we will find a reciprocal.
(Since 1/2 is the reciprocal of 2)