1
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Simplify the cube root of

2
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125, x to the sixth, y to the third power.

3
00:00:05,888 --> 00:00:08,051
So, taking the cube root of something

4
00:00:08,051 --> 00:00:10,089
is the same as raising that something

5
00:00:10,089 --> 00:00:11,451
to the one third power.

6
00:00:11,451 --> 00:00:13,301
So, this is equal to

7
00:00:13,301 --> 00:00:18,200
125, x to the sixth, y to the third power,

8
00:00:18,200 --> 00:00:21,498
raised to the one third power.

9
00:00:21,498 --> 00:00:23,618
And, if we take the product of a bunch of stuff

10
00:00:23,618 --> 00:00:25,210
and raise that to the one third power

11
00:00:25,210 --> 00:00:27,664
that's the same thing as individually raising

12
00:00:27,664 --> 00:00:29,267
each of the things to the one third power,

13
00:00:29,267 --> 00:00:31,003
and then taking the product.

14
00:00:31,003 --> 00:00:33,495
So this is going to be equal to

15
00:00:33,495 --> 00:00:36,325
125 to the one third power,

16
00:00:36,325 --> 00:00:40,511
times x to the sixth to the one third power,

17
00:00:40,527 --> 00:00:46,254
times y to the third to the one third power.

18
00:00:46,254 --> 00:00:50,085
And then, we can think about how we can simplify each of these.

19
00:00:50,085 --> 00:00:52,873
What is 125 to the one third?

20
00:00:52,888 --> 00:00:54,696
Well, let's just factor and see if we can have

21
00:00:54,696 --> 00:00:56,480
at least three prime factors of something,

22
00:00:56,480 --> 00:00:59,228
and maybe more than one prime factor

23
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that shows up three times.

24
00:01:00,531 --> 00:01:03,971
So, 125 is 5 times 25.

25
00:01:03,971 --> 00:01:07,200
25 is 5 times 5.

26
00:01:07,200 --> 00:01:10,521
So, 125 really is 5 times 5 times 5.

27
00:01:10,521 --> 00:01:14,513
So, if you multiply 5 times itself 3 times you get 125,

28
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or 125 to the 1/3 power is going to be 5.

29
00:01:18,803 --> 00:01:22,534
So, this is going to simplify to 5, times...

30
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And then, x to the sixth to the one third power...

31
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we saw this in a previous example.

32
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If you raise a base to an exponent,

33
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and then raise that whole thing to another exponent,

34
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you can take the product of the two exponents.

35
00:01:33,480 --> 00:01:38,555
So 6 times 1/3 is 6/3 or 2.

36
00:01:38,555 --> 00:01:41,360
So this part, right over here simplifies to

37
00:01:41,360 --> 00:01:44,115
x to the 6 divided by 3 power,

38
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or x squared.

39
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x squared.

40
00:01:47,772 --> 00:01:50,648
And then, finally over here, same principle:

41
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raising y to the third power

42
00:01:52,563 --> 00:01:54,935
and then that to the one third power.

43
00:01:54,935 --> 00:01:58,352
So, that's going to be y to the 3 to the 1/3 power,

44
00:01:58,352 --> 00:02:00,247
or y to the first power.

45
00:02:00,247 --> 00:02:02,505
And then times y.

46
00:02:02,505 --> 00:02:03,654
And we are done.

47
00:02:03,654 --> 00:02:06,147
And if you don't want to write this little multiplication here,

48
00:02:06,147 --> 00:02:12,938
you can just write this as 5, x squared, y.

49
00:02:12,938 --> 99:59:59,999
And we have simplified.