Evaluating expressions with variables: exponents
About this video
The video evaluates 5y^4 - y^2 when y = 3. It substitutes 3 for every y, uses the order of operations (PEMDAS) to work out the exponents first (3^4 = 81, 3^2 = 9), then multiplies (5 x 81 = 405) and finally subtracts to get 396.
You'll be able to
- substitute a value for a variable in an expression.
- evaluate powers such as 3^2 and 3^4 as repeated multiplication.
- use the order of operations to evaluate an expression with exponents.
Key words
- evaluate
- To work out the value of an expression.
- variable
- A letter, like y, that stands for a number.
- exponent
- The small raised number that tells you how many times to multiply a number by itself, as in 3^4 = 3 x 3 x 3 x 3.
- order of operations (PEMDAS)
- The rule for what to do first: parentheses, exponents, then multiplication and division, then addition and subtraction.
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.
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