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Evaluating expressions like 5x² & ⅓(6)ˣ

Evaluating expressions with exponents involves substituting a given value for the variable and following the order of operations. Calculate the exponent first, then perform any multiplication or division. Mastering this skill is essential for solving more complex algebraic problems and understanding mathematical relationships. Created by Sal Khan.

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Video transcript

- [Instructor] What I want you to do is evaluate the expression 5x squared when x is equal to three. Pause this video and have a go at that. All right, well, we just have to think about every place we see an x, we'll now replace it with a three. So this is going to be equivalent to five times, instead of x squared, it's going to be five times three squared. And we know from order of operations, we do the exponents first. That's why I actually put a parentheses around the three squared to just make that clear. And three squared is, of course, equal to nine and five times nine is equal to 45. Let's do another example that's a little bit different. Let's say I have the expression 1/3 times six to the x power, and I want to evaluate it when x is equal to two. Pause the video again and see if you can work that out. Well, once again, everywhere where we see an x, we'll replace that with a two. So this is going to be the same thing as 1/3 times six squared. Where we saw the x, we now replace that with a two. And so this is going to be equal to, we do the exponent first, order of operations, so it's going to be 1/3 times six squared is 36, and 1/3 of 36 is equal to 12. And we're done!