Evaluating exponential expressions

u11_l1_t1_we1 Evaluating exponential expressions

Evaluate the expression 5y to the 4th minus y squared when y is equal to 3

so every place you see a y here we can just replace it with a three

to evaluate it so it becomes 5 times three to the fourth power minus

three squared, all I did is every time we saw a y here, I put a three there

so what does this evaluate to, we have to remember our order of operations

remember parenthesis comes first, sometimes it's referred to as PEMDAS

P is for Parenthesis, E is for Exponents, M and D are for multiplication and

division and they are 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 should be P-E and then multiplication and division

are at the same level and addition and subtraction are at the same level

What this tells us is that we do parenthesis first and expeonentiation 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 have to evaluate is three squared

so just remember three to the first is three, it's just three times itself once

so it's just 3. Three squared is equal to three times three, three multiplied

by itself twice, thats equal to nine, three to the third power

is equal to three times three time three, or it can be viewed as

as three squared times three, so it would be nine, three times three

is nine, nine times three is equal to twenty seven, three to the fourth is

equal to three times three times three times three, three times three is nine

three times three is nine, so it's going to be the same thing as nine times nine

so it's going to be equal to eighty one. So we now know what

three to the fourth is, we know what three squared is

lets just put it in the expression, so this is going to be equal to

five times three to the fourth, three to the fourth is

eighty one, so five times eighty one, minus three squared, and we have three squared right over here it is

equal to nine. Five times eighty one minus nine, let's figure out what five times eighty one is,

so eighty one times five, one times five is five, eight times five is forty,

so this right over here is four hundred and five, so it becomes

four hundred and five minus nine, so that is going to be equal to

if we are subtracting ten it would be 395, but we're subtracting one less than that

so it's 396, and we're done.