Rules of Exponents-Applying them Together

[One speaker] 

[Screen has the following equation on the screen. ]

Narrator: In this video, we’ll demonstrate how to apply the rules of exponents together. This example has several different variables all being multiplied together and then all of them being raised to an exponent. Let’s break it down and use our order of operations and what we know about exponents to help us simplify this problem. First of all, according to the order of operations we need to do whatever we can inside these parenthesis first. Once we’ve simplified it as much as we can, then we can move on. The first thing I see within the parenthesis is there are terms with the same base being multiplied together within the parenthesis. Here I have M squared and I also have M to the 1. M by itself automatically means to the 1 power. I also have x cubed and mx to the one power. And finally there is a Y to the 1 power.

According to my rules for exponents with multiplication, I can add the exponents of the two M’s together. This becomes M to the 2, plus 1, 2 plus 1. Now I can do the same thing for the X variables. X to the 3 plus one. And finally I’m left with just Y to the 1.  [Writes, ] All of this is within the parenthesis and is still being squared. Not let’s simplify our exponents. We have M cubed because 2 plus 1 is 3, X to the 4th because 3 plus 1 is 4, all times Y, and all that is being squared. [Writes, ]

Now according to our rules of exponents, I can’t combine these anymore. This is as simplified as I can get everything within the parenthesis. Because these have different bases. I can’t just add their exponents. So now I’m going to apply my other rule of exponents. According to that rule, this is the same as M cubed all squared times X to the 4th all squared times Y squared. [Writes, ] Now, according to the rule of a term raised to an exponent that is also raised to an exponent, this becomes M to the 3 times 2 times x to the 4 times 2 times y, which is basically the one times 2, which is two, or squared. [Writes, ] So this whole problem is equal to M to the 6th power, X to the 8th power, y to the 2 power. [Writes continuing the previous equation, ] By following the order of operations and the rules of  exponents, we were able to simplify this expression down to this.

[End of video.]