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# Evaluating expressions with variables: exponents

CCSS.Math:

## Video transcript

evaluate the expression 5 Y to the fourth minus y squared when y is equal to three 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 -3 squared all I did is every time we saw Y here I put a 3 there every time we saw why I put a 3 so what does this evaluate to and we have to remember our order of operations remember parenthesis comes for sometimes it's referred to as PEMDAS let me write that down PEMDAS PEMDAS P is for parentheses he is for exponents m and D are for multiplication and division and at they're really at the same level of priority and then addition and subtraction at the same level if you really want to do it properly should be P E and then multiplication and division are really at the same level an 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 just 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're subtracting 10 it would be 395 but we're subtracting one less than that so it's 396 and we're done