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Evaluating exponent expressions with variables
- [Instructor] We are asked to evaluate the expression five to the x power minus three to the x power for x equals two. So pause this video, and see if you can figure out, what does this expression equal when x equals two? All right, now let's work through this together. So what we want to do is everywhere we see an x, we want to replace it with a two. So this expression, for x equals two, would be five to the second power minus three to the second power. Well, what's that going to be equal to? Well, five to the second power, that's the same thing as five times five. And then from that, we are going to subtract three times three, three times three. And now order of operations would tell us to do the multiplication or do the exponents first, which is this multiplication. But just to make it clear, I'll put some parentheses here. And this is going to be equal to, five times five is 25, minus nine, which is equal to, what's 25 minus nine? It is equal to 16. So that's what that expression equals for x equals two. Let's do another example. So now we are asked what is the value of y squared minus x to the fourth when y is equal to nine and x equals two? So once again, pause this video, and see if you can evaluate that. All right, so here we have variables as the bases, as opposed to being the exponents, and we have two different variables. But all we have to do is wherever we see a y, we substitute it with a nine. And wherever we see an x, we substitute it with a two. So y squared is going to be the same thing as nine squared minus, minus x, which is two. That minus looks a little bit funny, let me see. So this is gonna be nine squared minus x, which is two, two to the fourth power. Now what is this going to be equal to? Well, nine squared is nine times nine. So this whole thing is going to be equal to 81. This whole thing right over here is nine times nine. Nine times nine is that right over there. And then from that, we're going to subtract two to the fourth power. Well, what's two to the fourth power? That is two times two, times two, times two. So this is going to be, two times two is four, four times two is eight, eight times two is 16. So it's 81 minus 16. Now what is that going to be equal to? Let's see, 81 minus six is 75, and then minus another 10 is going to be 65. So there you have it, y squared minus x to the fourth, when y is equal to nine and x equals two, is equal to 65. And we're done.