We have one more pattern to cover with bases and exponents and this involves
division. I can think about expanding 3 to the 4th and 3 squared, just like
before. We can simplify common factors in the numerator and denominator. They
make 1. Because we're working with a fraction made up of factors, we know these
make 1. So we're left with 3 times 3, or 3 squared. We can think about expanding
these variables as well. We simplify common factors in the numerator and in the
denominator, and we're left with f to the 3rd. This last one is just like the
others before except we needed to do something additional for the two numbers or
coefficients. I know 6 divides into 12 and 6 divides into 18. 6 into 12 is 2,
and 6 into 18 is 3. So I have 2 3rds times w to the 5th. I've showed you the
expanded form, and the simplification, so that way we could look at the pattern.
What's happening as we move from the left side to the right side? What do you
notice about the exponents? Let's see if you can answer this with a question.
What's a rule for the pattern that you see over here? You can write your answer
in this box. And be sure that it includes a base of x, and involves your
exponents a and b. What'd you do with them?