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### Course: 6th grade > Unit 6

Lesson 4: Substitution & evaluating expressions- Evaluating an expression with one variable
- Evaluating expressions with one variable
- Evaluating exponent expressions with variables
- Evaluating expressions like 5x² & ⅓(6)ˣ
- Variable expressions with exponents
- Evaluating expressions with one variable

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# Evaluating exponent expressions with variables

In this math lesson, we learn to evaluate expressions with exponents and variables. We practice substituting values for variables and calculating the results. By mastering this skill, we can solve problems involving exponential expressions, enhancing our understanding of algebra and mathematical concepts.

## Want to join the conversation?

- What is (x+4)^2 = 25x^2? There need to be 2 answers.(46 votes)
- First, work out the expression to a form of ax^2 + bx + c = 0
`25x^2 – (x^2 + 8x + 16) = 0`

25x^2 – x^2 – 8x – 16 = 0

24x^2 – 8x – 16 = 0

Now, since 0 / n = 0, we can divide both sides by the shared factor of 8 among the terms

3x^2 – x – 2 = 0

The fact that a is not equal to 1 makes manual solving a little harder, but trying a few integer combinations gives us:`(3x + 2)(x – 1) = 3x^2 – 3x + 2x – 2`

= 3x^2 – x – 2

3x + 2 = 0 or x – 1 = 0

3x = -2 or x = 1

x = -2/3 or x = 1(22 votes)

- It still doesn't make sense to me because how does four twos make 16? Doesn't it equal 8?

Someone please reply and help me i'm so confused(13 votes)- Four two's does equal 8. But 2 times 2 times 2 times 2 is equal to 16.(9 votes)

- if a tomato is a fruit, then is ketchup a smoothie?(11 votes)
- It's a puree!(9 votes)

- At0:51, wouldn't the -3^3 actually be -3*-3?

If the problem had parenthesis around the 3^2 then it would be 3*3.(9 votes)- The problem has
`-3^2`

, not -3^3.

PEMDAS rules tell us the exponent must be done before the minus sign.

`-3^2`

=`- (3 * 3)`

=`-9`

For the exponent to apply to the minus sign, the problem would need parentheses:`(-3)^2`

See this video for more info: https://www.khanacademy.org/math/in-seventh-grade-math/exponents-powers/laws-exponents-examples/v/exponents-with-negative-bases(9 votes)

- I'm so proud of myself for being able to solve these independently. When he tells us to pause the video, I can actually solve it with no explanation!(12 votes)
- At0:51, wouldn't the -3^3 actually be 2*3?(5 votes)
- It is 5^2-3^2, and exponents are repeated multiplication of the base, since base is 3, you multiply the base (3) the number of times of the expnnent (2). Thus, -3^2=-(3*3)=-9.(11 votes)

- 5-3=2, ^2+^2=^4, 2^4=16 but does it always work?(4 votes)
- You can't carry over a base and use the exponentiation symbol multiple times. Think of it like eating a banana. Your banana is gone after the operation; you'll need to get another one for the next operation, even if it's the same operation and the same banana.

Correct syntax would be:`5 - 3 = 2.`

2^2 + 2^2 = 2*(2^2) = 2^1 * 2^2

= 2^(2 + 1)

[This is called the "product rule" of exponentation; b^p * b^q = b^(p + q)]

This is equal to 8, not 16! Also, the answer would've been no if it were true; you'd need to repeat the addition process the same amount of times as your exponent base for this to work!(10 votes)

- can you teach step by step SLOWLY?(4 votes)
- You can lower the speed if you make it the full player, since it will become YouTube like programmed.(7 votes)

- If you have a fraction

such as 8^2/2^4

can you first do the exponents and then find the value?(5 votes)- Yep, that's quite right! However, to use the division rule of exponents, you must use the same base. We can take the greatest common divisor of the different bases and make this our new base!

2^(3*2) / 2^4 = 2^(6 - 4) = 2^2 = 4(4 votes)

- When we are using variables with exponents , we do it normally and put the missing numbers in place of the variable?(4 votes)

## Video transcript

- [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.