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# Evaluating expressions with variables: exponents

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.