About this video
To evaluate an expression with an exponent, replace every x with the given value, then follow the order of operations: do the exponent first, then multiply. The video evaluates 5x^2 when x = 3 (giving 45) and 1/3 × 6^x when x = 2 (giving 12).
You'll be able to
- substitute a value for x in an expression with an exponent.
- use the order of operations to do exponents before multiplying.
- evaluate expressions where the variable is the exponent, like 6^x.
Key words
- evaluate
- To find the value of an expression after replacing the variable with a number.
- exponent
- A small raised number that tells you how many times to multiply a number by itself, like the 2 in 3^2.
- order of operations
- The agreed order for doing calculations: brackets, then exponents, then multiplication and division, then addition and subtraction.
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!
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.