What is (x+4)^2 = 25x^2? There need to be 2 answers.

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

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

Four two's does equal 8. But 2 times 2 times 2 times 2 is equal to 16.

At 0:51, wouldn't the -3^3 actually be -3*-3? If the problem had parenthesis around the 3^2 then it would be 3*3.

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

If you have a fraction such as 8^2/2^4 can you first do the exponents and then find the value?

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

At 0:51, wouldn't the -3^3 actually be 2*3?

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.

5-3=2, ^2+^2=^4, 2^4=16 but does it always work?

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!

can you teach step by step SLOWLY?

You can lower the speed if you make it the full player, since it will become YouTube like programmed.

when evaluating 5 to the 3rd minus 3 to the second, why doesn't the 3 actually equal negative three making it 25 + 9 = 34?

Well, the minus sign represents subtraction and not negative value, and when if it represents negative value, it's typically in parentheses when next to the minus sign. Hope it helps :D

Main content

6th grade

Course: 6th grade > Unit 6

Lesson 4: Substitution & evaluating expressions

Evaluating exponent expressions with variables

Name: Evaluating exponent expressions with variables
Uploaded: 2017-10-30T15:32:53Z
Description: 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.

Google Classroom

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.

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Aurora
Posted 6 years ago. Direct link to Aurora's post “What is (x+4)^2 = 25x^2? ...”
What is (x+4)^2 = 25x^2? There need to be 2 answers.
Button navigates to signup pageComment on Aurora's post “What is (x+4)^2 = 25x^2? ...”
(41 votes)
Answer
- Ralph Schraven
  Posted 4 years ago. Direct link to Ralph Schraven's post “First, work out the expre...”
  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
  Comment on Ralph Schraven's post “First, work out the expre...”
  (17 votes)
Claudia
Posted 4 years ago. Direct link to Claudia's post “It still doesn't make sen...”
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
Button navigates to signup pageComment on Claudia's post “It still doesn't make sen...”
(10 votes)
Answer
- T H A N O S
  Posted 4 years ago. Direct link to T H A N O S's post “Four two's does equal 8. ...”
  Four two's does equal 8. But 2 times 2 times 2 times 2 is equal to 16.
  Comment on T H A N O S's post “Four two's does equal 8. ...”
  (9 votes)
Jon Kathman
Posted 5 years ago. Direct link to Jon Kathman's post “At 0:51, wouldn't the -3^...”
At
0:51
, wouldn't the -3^3 actually be -3*-3?
If the problem had parenthesis around the 3^2 then it would be 3*3.
Button navigates to signup pageButton navigates to signup page
(8 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “The problem has `-3^2`, n...”
  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
  Button navigates to signup page
  (8 votes)
Ankush Roy😀🤺
Posted a year ago. Direct link to Ankush Roy😀🤺's post “At 0:51, wouldn't the -3...”
At
0:51
, wouldn't the -3^3 actually be 2*3?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- David Severin
  Posted a year ago. Direct link to David Severin's post “It is 5^2-3^2, and expone...”
  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.
  Comment on David Severin's post “It is 5^2-3^2, and expone...”
  (11 votes)
nigel.everson
Posted 4 years ago. Direct link to nigel.everson's post “5-3=2, ^2+^2=^4, 2^4=16 b...”
5-3=2, ^2+^2=^4, 2^4=16 but does it always work?
Button navigates to signup pageComment on nigel.everson's post “5-3=2, ^2+^2=^4, 2^4=16 b...”
(3 votes)
Answer
- Ralph Schraven
  Posted 4 years ago. Direct link to Ralph Schraven's post “You can't carry over a ba...”
  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!
  Button navigates to signup page
  (9 votes)
pEyToN nOrToN
Posted 4 years ago. Direct link to pEyToN nOrToN's post “If you have a fraction su...”
If you have a fraction
such as 8^2/2^4
can you first do the exponents and then find the value?
Button navigates to signup pageComment on pEyToN nOrToN's post “If you have a fraction su...”
(5 votes)
Answer
- Ralph Schraven
  Posted 3 years ago. Direct link to Ralph Schraven's post “Yep, that's quite right! ...”
  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
  Comment on Ralph Schraven's post “Yep, that's quite right! ...”
  (4 votes)
NABAAJASSAM2004
Posted 5 years ago. Direct link to NABAAJASSAM2004's post “can you teach step by ste...”
can you teach step by step SLOWLY?
Button navigates to signup pageComment on NABAAJASSAM2004's post “can you teach step by ste...”
(3 votes)
Answer
- Sara Lynn Younes
  Posted 4 years ago. Direct link to Sara Lynn Younes's post “You can lower the speed i...”
  You can lower the speed if you make it the full player, since it will become YouTube like programmed.
  Button navigates to signup page
  (6 votes)
IMJST
Posted 2 years ago. Direct link to IMJST's post “It equals to 25-9”
It equals to 25-9
Button navigates to signup pageComment on IMJST's post “It equals to 25-9”
(5 votes)
Answer
hailey
Posted 15 days ago. Direct link to hailey's post “I'm so proud of myself fo...”
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!
Button navigates to signup pageComment on hailey's post “I'm so proud of myself fo...”
(4 votes)
Answer
Ashley Jackson
Posted 2 months ago. Direct link to Ashley Jackson's post “when evaluating 5 to the ...”
when evaluating 5 to the 3rd minus 3 to the second, why doesn't the 3 actually equal negative three making it 25 + 9 = 34?
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- Loaf
  Posted 2 months ago. Direct link to Loaf's post “Well, the minus sign rep...”
  Well, the minus sign represents subtraction and not negative value, and when if it represents negative value, it's typically in parentheses when next to the minus sign.
  
  Hope it helps :D
  Button navigates to signup page
  (8 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.