Welcome back, everyone. We saw how to simplify expressions by combining like terms. For example, in this expression, we could combine
So it turns out that when this happens and we can't combine like terms, we're going to need some new rules to simplify expressions that have exponents in them. What I'm going to do in this video is show you by using all these rules we're going to talk about that this expression actually just simplifies down to something like
Let's just go ahead and get started here. So let's say I had something like
Alright. So that's a pretty straightforward one. It's called the base one rule. The names are the least important thing about the rule. It's just really important that you learn how they work.
Let's go ahead and move on to the second one here, a negative to an even power. So let's say I had negative three squared. That just means negative three and negative three.
Well, as long as you have a pair of negative signs, the negative sign always just gets canceled out. It doesn't matter if the exponent is
Now let's see what happens when you have negatives raised to odd powers, something like
Well, this gets canceled out with this one. But what about this one? This third negative sign doesn't have another one to cancel it out the negative, so it actually just gets kept there. So this is
Whenever you have a negative to an odd power, you actually end up keeping the negative sign on the outside. So you keep the negative sign here. Alright. So pretty straightforward. Let's take a look at another couple of rules here.
Now we're going to get into, like, multiplication and division. Let's see what happens when you have something like
It's all multiplication. So it's basically like I just have
Anytime you're multiplying numbers of the same base, you actually just add their exponents together. So when you multiply, you add. One way you can kind of remember this is that the multiplication symbol and the addition symbol, they kind of just look alike, but one is tilted. So it's an easy, silly way to remember this. But that actually turns out to be a really, really important rule and a shortcut because sometimes you're going to have expressions where you don't want to write out all the terms like
This actually just ends up being
So it's not
Alright. So here we actually ended up adding the exponents, but here to get the
So when you divide, you subtract. And one way to remember this is that you're doing division, which kind of looks like a little minus sign, so division is subtraction. Now one tiny difference here is that when you added the exponents, the order doesn't matter because
Alright? So that's really important. Don't mess that up. Alright, everyone. So that's it for the first couple of rules.
We'll take a look at more later on. Let's get some practice with these rules over here. We're going to simplify these expressions by using the exponent rules. Let's take a look at the first one. We have
So in other words, we have the same base that's being divided with different exponents. That just means we're going to use the quotient rule and we're going to subtract the exponents. Alright? So in other words, we're going to take this and this is going to be
But remember, this actually is now a negative number raised to an odd power, so we can use the negative to odd power rule, and we keep the negative sign on the outside. And then if we wanted to evaluate this as a single number, this would just be
We have
So in other words, you're multiplying numbers or terms of the same base. So that means we can actually add their exponents. So the
So now we can use the quotient rule for this, and we subtract the exponents. In other words, this is just
Let's go take a look at the third one. Here we have just multiplication of a bunch of these terms here. We could do the exact same thing that we did with the numerator in this term. Everything is multiplied. There's no division.
So the