The main things to remember about zero and and negative exponents are that 1) anything raised to the zero power is 1, and 2) to simplify an expression with negative exponents, take the reciprocal of the base (i.e., if it is in the numerator then move it to the denominator, if it's in the denominator then move it to the numerator) and change the sign of the exponent.
Here to solve this problem we’re going to have to use some of the new ideas about exponents because we have some zeros and we have some negative exponents. Before we start I want to point out something that I did when I wrote this problem, I wrote z with a little slash through it because if I were to write z like this it might look like a 2. It’s up to you if you want to do that. A lot of times in other countries whenever they write z they do that slashy guy. It’s up to you if you want to do that when you’re writing the problem.
Okay. So I’m going to work through this problem one variable at a time. X to the -4 power means I’m going to have 1/x to the 4th. The negative kicks it into the bottom of the fraction and that exponent becomes positive. That part’s done.
Y to the zero power; well anything to the zero power is equal to one, so that guy I don’t need to write in my answer. I’m not going to have any y terms in my answer here. And then z to the 6th is gong to stay on top of the fraction. So if I want to, I could write 1z to the 6th or that 1 doesn’t need to be there. I could just write z to the 6th.
So this is my final answer, z to the 6th over x to the 4th. Who knew that that funny product would end up as that quotient? In order to be able to do these kinds of problems, you have to remember the properties of exponents when they are negative and also when you have a zero. If you can keep that stuff straight these problems are pretty quick and they don’t require a lot of writing which I like.
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M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
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