﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.01,0:00:03.86,Default,,0000,0000,0000,,We have one more pattern to cover with bases and exponents and this involves Dialogue: 0,0:00:03.86,0:00:07.82,Default,,0000,0000,0000,,division. I can think about expanding 3 to the 4th and 3 squared, just like Dialogue: 0,0:00:07.82,0:00:12.00,Default,,0000,0000,0000,,before. We can simplify common factors in the numerator and denominator. They Dialogue: 0,0:00:12.00,0:00:16.24,Default,,0000,0000,0000,,make 1. Because we're working with a fraction made up of factors, we know these Dialogue: 0,0:00:16.24,0:00:20.82,Default,,0000,0000,0000,,make 1. So we're left with 3 times 3, or 3 squared. We can think about expanding Dialogue: 0,0:00:20.82,0:00:25.62,Default,,0000,0000,0000,,these variables as well. We simplify common factors in the numerator and in the Dialogue: 0,0:00:25.62,0:00:30.10,Default,,0000,0000,0000,,denominator, and we're left with f to the 3rd. This last one is just like the Dialogue: 0,0:00:30.10,0:00:34.66,Default,,0000,0000,0000,,others before except we needed to do something additional for the two numbers or Dialogue: 0,0:00:34.66,0:00:39.24,Default,,0000,0000,0000,,coefficients. I know 6 divides into 12 and 6 divides into 18. 6 into 12 is 2, Dialogue: 0,0:00:39.24,0:00:43.59,Default,,0000,0000,0000,,and 6 into 18 is 3. So I have 2 3rds times w to the 5th. I've showed you the Dialogue: 0,0:00:43.59,0:00:47.66,Default,,0000,0000,0000,,expanded form, and the simplification, so that way we could look at the pattern. Dialogue: 0,0:00:47.66,0:00:51.78,Default,,0000,0000,0000,,What's happening as we move from the left side to the right side? What do you Dialogue: 0,0:00:51.78,0:00:56.04,Default,,0000,0000,0000,,notice about the exponents? Let's see if you can answer this with a question. Dialogue: 0,0:00:56.04,0:01:00.56,Default,,0000,0000,0000,,What's a rule for the pattern that you see over here? You can write your answer Dialogue: 0,0:01:00.56,0:01:04.59,Default,,0000,0000,0000,,in this box. And be sure that it includes a base of x, and involves your Dialogue: 0,0:01:04.59,0:01:07.07,Default,,0000,0000,0000,,exponents a and b. What'd you do with them?