Lesson 10: Product Rule #3

Narrator: We are asked to simplify the following expressions. [m3x6m] And by simplifying what we are going to do is find those terms that have the same base and combine them. Now let's remember what the product rule tells us. The product rule says that when we have the same base raised to an exponent. That we can add our exponents. So in this problem we are going to do that and we are going to find those that have the same base. Now let's also remember that when we are doing multiplication, the order doesn't matter. So I can rewrite this problem as m to the third power times m times x to the sixth power and I'm just going to do that just so I can see that I have my bases that are the same next to each other. And now I also want to recall that anything raised to the first power is just itself so I can rewrite this as m to the third power times m to the first power times x to the sixth power. And now I can add my exponent so I have m raised to the third plus one power times x to the sixth power. And then I can rewrite that as m to the fourth times x to the sixth. And if I need to see that broken down better you can see that m to the third is m times m times m and then we have one more m times x to the sixth which would be x times x times x times x times x times x. And now if I combine those I can see 1, 2, 3, 4 and that can be written as m to the fourth. And 1, 2, 3, 4, 5, 6 and thats x to the sixth which is what we got over here. So our answer is m raised to the fourth times x raised to the sixth.

[End of video]