1
00:00:00,302 --> 00:00:07,400
Evaluate the expression 5y to the 4th minus y squared when y is equal to 3

2
00:00:07,400 --> 00:00:10,733
so every place you see a y here we can just replace it with a three

3
00:00:10,733 --> 00:00:17,467
to evaluate it so it becomes 5 times three to the fourth power minus

4
00:00:17,467 --> 00:00:24,892
three squared, all I did is every time we saw a y here, I put a three there

5
00:00:24,892 --> 00:00:28,400
so what does this evaluate to, we have to remember our order of operations

6
00:00:28,400 --> 00:00:36,272
remember parenthesis comes first, sometimes it's referred to as PEMDAS

7
00:00:36,272 --> 00:00:39,795
P is for Parenthesis, E is for Exponents, M and D are for multiplication and

8
00:00:39,795 --> 00:00:44,333
division and they are really at the same level of priority and then addition

9
00:00:44,333 --> 00:00:46,324
and subtraction are at the same level. If you really

10
00:00:46,324 --> 00:00:50,410
want to do it properly should be P-E and then multiplication and division

11
00:00:50,410 --> 00:00:54,241
are at the same level and addition and subtraction are at the same level

12
00:00:54,400 --> 00:00:59,000
What this tells us is that we do parenthesis first and expeonentiation takes

13
00:00:59,000 --> 00:01:02,800
priority over everything else here, so we have to evaluate these exponents

14
00:01:02,800 --> 00:01:05,898
before we multiply anything or before we subtract anything.

15
00:01:05,898 --> 00:01:09,000
So the one exponent we have to evaluate is three squared

16
00:01:09,000 --> 00:01:13,867
so just remember three to the first is three, it's just three times itself once

17
00:01:13,867 --> 00:01:19,133
so it's just 3. Three squared is equal to three times three, three multiplied

18
00:01:19,133 --> 00:01:24,333
by itself twice, thats equal to nine, three to the third power

19
00:01:24,333 --> 00:01:28,816
is equal to three times three time three, or it can be viewed as

20
00:01:28,816 --> 00:01:32,230
as three squared times three, so it would be nine, three times three

21
00:01:32,230 --> 00:01:36,600
is nine, nine times three is equal to twenty seven, three to the fourth is

22
00:01:36,600 --> 00:01:43,561
equal to three times three times three times three, three times three is nine

23
00:01:43,561 --> 00:01:48,000
three times three is nine, so it's going to be the same thing as nine times nine

24
00:01:48,000 --> 00:01:51,224
so it's going to be equal to eighty one. So we now know what

25
00:01:51,224 --> 00:01:53,333
three to the fourth is, we know what three squared is

26
00:01:53,333 --> 00:01:56,216
lets just put it in the expression, so this is going to be equal to

27
00:01:56,216 --> 00:01:59,606
five times three to the fourth, three to the fourth is

28
00:01:59,606 --> 00:02:08,667
eighty one, so five times eighty one, minus three squared, and we have three squared right over here it is

29
00:02:08,667 --> 00:02:14,676
equal to nine. Five times eighty one minus nine, let's figure out what five times eighty one is,

30
00:02:14,676 --> 00:02:21,467
so eighty one times five, one times five is five, eight times five is forty,

31
00:02:21,467 --> 00:02:26,000
so this right over here is four hundred and five, so it becomes

32
00:02:26,000 --> 00:02:31,467
four hundred and five minus nine, so that is going to be equal to

33
00:02:31,467 --> 00:02:35,867
if we are subtracting ten it would be 395, but we're subtracting one less than that

34
00:02:35,867 --> 99:59:59,999
so it's 396, and we're done.