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## 6th grade (Illustrative Mathematics)

### Course: 6th grade (Illustrative Mathematics) > Unit 6

Lesson 15: Lesson 15: Equivalent exponential expressions# Evaluating expressions like 5x² & ⅓(6)ˣ

We work through a few examples showing how to evaluate some common expressions we see involving variables, exponents, and fractions. Created by Sal Khan.

## Want to join the conversation?

- How does 1/3 x 36 = 12?(5 votes)
- 1 * 36 = 36

3 * 1 = 3

Since 36 = 36/1, 1*36 / 3*1 is the same thing as saying 36/3, or 12.

Or, think of it this way: 1/3 * 36 is the same as 36 / 3, which is also 12.(6 votes)

- WHAT IS 6^2 + x - x^26

2

+x−x

2

6, squared, plus, x, minus, x, squared for x=3x=3x, equals, 3.(3 votes)- It appears you tried to copy and paste a question, but the syntax is so confusing, it is difficult to tell what you are really asking.(4 votes)

- How it equals 12 is because they did 36 divided by 3 = 12(3 votes)
- 36/3 = 12 can be simplified to (30/3 + 6/3)

which gives you 10 + 2, which is equal to 12.(1 vote)

- So every time you see an x that’s immediately three? This is so confusing!(0 votes)
- No, the question will say what x equals.

Ex. 5x when x=4, you will change x into 4 and get the question 5x4=20(7 votes)

- I need help I am confused with fractions and exponents.

What do with other fractions.(3 votes) - At the second question with thirds how do you do like thirds,half's and quarters. Do you divide your number by like thirds if it was thirds? For example 1/2 5 do you divide by half’s? I don’t think sal said anything about that.(2 votes)
- no you divide by 2 when you multiply by 1/2(3 votes)

- you have to to equal 3(2 votes)

- so how do u find out what x is if the problem didnt say the answer(1 vote)
- You cannot evaluate an expression unless they give you value(s) to put in. without the value(s), it just remains an expression.(2 votes)

## 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!