WEBVTT 00:00:00.290 --> 00:00:03.128 Let's go through some more exponent examples. 00:00:03.128 --> 00:00:06.487 So to warm up, let's think about taking a fraction to some power. 00:00:06.487 --> 00:00:14.527 So let's say I have two-thirds (2/3), and I want to raise it to the 3rd power here. 00:00:14.527 --> 00:00:16.958 And we've already learned there are two ways of thinking about this. 00:00:16.958 --> 00:00:19.885 One way is to say let's take three 2/3's – 00:00:19.885 --> 00:00:26.339 So that's one 2/3rd, two 2/3's, and three 2/3's. 00:00:26.339 --> 00:00:29.719 So that's (COUNTING: One, two) three 2/3's. 00:00:29.719 --> 00:00:34.231 And then we multiply them. 00:00:34.231 --> 00:00:37.170 And we will get, let's see – 00:00:37.170 --> 00:00:40.746 The numerator will be 2 × 2 × 2, which is 8. 00:00:40.746 --> 00:00:47.098 And the denominator's going to be 3 × 3 × 3, which is equal to 27. 00:00:47.098 --> 00:00:53.891 Now the other way of viewing this is you start with a 1 and you multiply it by 2/3 three times. 00:00:53.891 --> 00:00:56.963 So you multiply by 2/3 once, twice, three times. 00:00:56.963 --> 00:00:59.901 You will get the exact same result here. 00:00:59.901 --> 00:01:01.837 So let's do one more example like that. 00:01:01.837 --> 00:01:05.869 So lets say I had 4/9, and I want to square it. 00:01:05.869 --> 00:01:08.676 When I raise something to the second power, people often say, "You're squaring it." 00:01:08.676 --> 00:01:12.846 Also when you're raising something to the 3rd power, people sometimes say, "You're cubing it." 00:01:12.846 --> 00:01:15.964 But let's raise 4/9 to the 2nd power. Let's square it. 00:01:15.964 --> 00:01:19.626 I encourage you to pause the video and work this out yourself. 00:01:19.626 --> 00:01:26.989 Well, once again, you could view this as taking two 4/9's and multiplying them. 00:01:26.989 --> 00:01:32.741 Or you could view this as starting with a 1, and multiplying it by 4/9 two times. 00:01:32.741 --> 00:01:37.470 Either way, your numerator is going to be 4 × 4, which is 16. 00:01:37.470 --> 00:01:45.498 And your denominator is going to be 9 × 9, which is equal to 81.