Evaluating exponent expressions with variables

We are asked to evaluate the expression (5) to the (x) power minus (3) to the (x) power for (x) equals (2). So pause this video and see if you can figure out what hap—what does this expression equal when (x) equals (2).

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 (2). So this expression for (x) equals (2) would be (5) to the second power minus (3) to the second power.

Well, what's that going to be equal to? Well, (5) to the second power that's the same thing as (5) times (5), and then from that, we are going to subtract (3) times (3). 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 (5) times (5) is (25) minus (9), which is equal to plus (25) minus (9). It is equal to (16). So that's what that expression equals for (x) equals (2).

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 (9) and (x) equals (2). So once again pause this video and see if you can evaluate that.

All right, so here we are. 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 (9), and wherever we see an (x), we substitute it with a (2).

So (y) squared is going to be the same thing as (9) squared minus—minus (x), which is (2). That minus looks a bit funny; let me see. So this is going to be (9) squared minus (x), which is (2) to the fourth power.

Now, what is this going to be equal to? Well, (9) squared is (9) times (9). So this whole thing is going to be equal to (81). This whole thing right over here is (9) times (9); (9) times (9) is that right over there, and then from that, we're going to subtract (2) to the fourth power.

Well, what's (2) to the fourth power? That is (2) times (2) times (2) times (2). So this is going to be (2) times (2) is (4), (4) times (2) is (8), and (8) times (2) is (16). So it's (81) minus (16).

Now what is that going to be equal to? Let's see. (81) minus (6) 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 (9) and (x) equals (2) is equal to (65), and we're done.