In Exercises 107–114, simplify each exponential expression. Assum...

Question

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3

Accepted Answer

Welcome back. Let's look at our next problem. It says consider the given exponential expression and then simplify. So we've got an expression with two terms multiplied two multiplied to each other. The first one being eight M. To the minus five. N. P. To the minus eight. And the second term is eight M. In parentheses all to the minus five power. So I'm going to rewrite these terms just to distribute out that exponent outside the parentheses. So my first term I just rewrite here the same way and my second term is now eight to the minus five M. To the minus five. So distribute that exponent there. Now I want to combine like terms to multiply these two terms together. Well the only number here I have is a base is eight. So to sort of help me remember in this first term I'm going to write the eight as eight to the one power because I'm remembering that if I have the same base and it's raised to a power and I'm multiplying those two terms, I add the exponents. So remembering that X. To the A. Times X. To the B. Power equals X. To the A. Plus B. So using writing that is 8 to the one that helps me remember that. So let me move on to my next line. I'm just going to change colors. Keep track somebody combined my eights here and we write that as eight to the one plus negative five. So eight to the negative four power. Then I'm gonna combine my M terms here and I get em to the negative five plus negative five which equals M to the negative 10 power. And then my np terms there's only one set of them. So I just rewrite them N. P. To the minus eight. Now I'm gonna go on to the next line to simplify that, remembering that when I have a negative negative exponent. So X. To the negative A. Equals one over X. To the A. The reciprocal Of the # two. The positive power. So let's rewrite this remembering that. Well the only uh term in here that's not too negative power is my end. So the only thing in the numerator here is going to be n. Now quick test taking tip. If I were in a hurry I might check back at this point. I see that only one of my answer choices has end by itself in the numerator and that's choice A. So if time is of the essence I could mark A. Is my answer and just move on. That's the only one I'm going to be thorough and work all the way through. But just keep that in mind when you're solving kind of a long thing like this. And if you're in a hurry it's good to check back on your answers sort of halfway through and see if you can eliminate any of them. So but here we're gonna go ahead and make sure that's correct and we go through. So our negative exponents. We put in the denominator. I have eight to the minus four. Now I can do the math but I see all four of my answers. The only number here is 4096 so I could dress that. That's eight to the fourth power. So 4096 goes in the denominator now. M. To the 10th power in the denominator and then P. To the eighth power. And sure enough choice A matches that N. Over 4096. M. To the 10th power, P. To the eighth power. So that's my answer. See you in the next video.

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