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Evaluating expressions with variables: exponents

In this math lesson, we learn to evaluate an algebraic expression with exponents by following the order of operations (PEMDAS). We substitute a given value for the variable, calculate exponents, perform multiplication, and finally, subtraction. By applying these steps, we successfully find the value of the expression. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • blobby green style avatar for user Christopher Sanders
    how do you do a problem when they don' t give you what a letter is?
    Like this 62 A13-2 10
    (12 votes)
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    • duskpin ultimate style avatar for user Kelly McMahan
      It is not possible to algebraically solve a problem if they do not give you the value of the letter. The best you can do is to simplify the equation, which would mean that you use PEMDAS on all of the numbers, and the variable would have to stay. However, if the number set you gave were to equal something , then it would be possible to find A, but without that, you cannot solve a problem if they do not give you what the letter is. Hope this helps :) ask if you have any other questions!
      (32 votes)
  • marcimus pink style avatar for user Diya Upadhyaya
    At around 51 seconds Sal tells us that addition and subtraction and multiplication and division are at the same level then why is it PEMDAS not PEDMSA
    (4 votes)
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    • stelly blue style avatar for user Kim Seidel
      PEMDAS has 4 rules, not 6.
      1) P = Parentheses. Do all work inside the parentheses as your 1st step
      2) E = Exponents. All exponents come next
      3) MD = Multiply & divide. These are in the same rule. You always work left to right within the rule. Example: 8/2*6 = 4*6 = 24. Division is done 1st because it is on the left.
      4) AS = Add & Subtract. Again, these are in the same rule. You need to work left to right.

      So, Sal's statement is correct. He is trying to explain / remind us that there are only 4 rules, not 6.
      Hope this helps.
      (20 votes)
  • orange juice squid orange style avatar for user Unpotato
    At , Sal replaces the Y into the equation. What is the logic behind NOT taking all of 5y to the fourth?
    (7 votes)
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  • piceratops seed style avatar for user Kivi Mayfield
    PEMDAS can be remembered as
    Parentheses ( ) Please
    Exponents 2* Excuse
    Multiplication x My
    Division / Dear
    Addition + Aunt
    Subtraction - Sally
    or if your older some teachers recommend GEMDAS same thing but the "G" stands grouping symbols "[]" and then parentheses
    3* 4+[ 89 + 3(56+3) * (-5%)
    A real life problem above; see if you can solve !
    Hope this helps !
    (9 votes)
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  • blobby green style avatar for user writeranom
    In evaluating 5y^4-y^2= 5(3)^4-3^2, how come the negative sign was not considered when computing for 3^2 instead of being -3^2? This confused me as I assumed since the negative symbol before a number would require to evaluate it as a negative. Doing that would give an answer of 414 and not 396 since the equation would change to 5(81)+9 no?
    (6 votes)
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  • hopper happy style avatar for user sukhmani
    I need help with a question that doesn't have anything to do with topic but it would be nice if someone helped me.

    A wetsuit cost one third of the cost of diving gear. David hires a wetsuit and diving gear for the same time and length and pays $144 in total.
    How much money did david spend on the wetsuit in dollars.
    (7 votes)
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  • blobby green style avatar for user Angie Ramirez
    40+40x0+1 =
    I'm doing it like this 40+(40x0)+1 =41 is this correct
    (4 votes)
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  • blobby green style avatar for user Ariez.Ortiz
    Khan Academy is so fun you just have to put some effort into it.
    (6 votes)
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  • blobby green style avatar for user Sam Eaton
    For quiz/practice questions students really should be told how Khan would like the answers. Do they want fractions or do they want decimal answers? After several "wrong" answers to a question we figured out they wanted a fraction.
    (3 votes)
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    • leaf grey style avatar for user Eve Georgoulias
      usually they want it as the fraction/decimal is displayed in the problem. For example if they use decimals in the equations or title of the practice then most likely it will want decimal answers. I know this can be frustrating especially the equations with both, but it will allow you to retake the quiz so you can get the right answers and a good score
      Hope this helps!
      (5 votes)
  • blobby green style avatar for user randall.phelps
    help me
    (4 votes)
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Video transcript

Evaluate the expression 5y to the fourth minus y squared when y is equal to 3. So every place we see a y here, we could just replace it with a 3 to evaluate it. So it becomes 5 times 3 to the fourth power minus 3 squared. All I did is every time we saw a y here, I put a 3 there. Every time we saw a y, I put a 3. So what does this evaluate to? And we have to remember our order of operations. Remember, parentheses comes first. Sometimes it's referred to as PEMDAS. Let me write that down. PEMDAS, PEMDAS. P is for parentheses. E is for exponents. M and D are for Multiplication and Division. They're really at the same level of priority. And then addition and subtraction are at the same level. If you really want to do it properly, it should be P-E, and then multiplication and division are really at the same level. And addition and subtraction are at the same level. But what this tells us is that we do parentheses first. But then after that, exponentiation takes priority over everything else here. So we have to evaluate these exponents before we multiply anything or before we subtract anything. So the one exponent we'd have to evaluate is 3 squared. So let's remember. 3 to the first is just 3. It's just 3 times itself once. So it's just 3. 3 squared is equal to 3 times 3, 3 multiplied by itself twice. That's equal to 9. 3 to the third power is equal to 3 times 3 times 3. Or you could view it as 3 squared times 3. So it'll be 9. 3 times 3 is 9. 9 times 3 is equal to 27. 3 to the fourth is equal to 3 times 3 times 3 times 3. So 3 times 3 is 9. 3 times 3 is 9. So it's going to be the same thing as 9 times 9. So this is going to be equal to 81. So we now know what 3 to the fourth is. We know what 3 squared is. Let's just put it in the expression. So this is going to be equal to 5 times 3 to the fourth. 3 to the fourth is 81. So 5 times 81 minus 3 squared. And we have 3 squared right over here. It is equal to 9. 5 times 81 minus 9. Let's figure out what 5 times 81 is. So 81 times 5. 1 times 5 is 5. 8 times 5 is 40. So this right over here is 405. So it becomes 405 minus 9. So that is going to be equal to-- if we were subtracting 10, it would be 395. But we're subtracting one less than that. So it's 396. And we're done.