# Welcome to Algebra I: Quotient of Powers

28 minutes

(female narrator) G to the 5th, H to the 4th, K to the 3rd. Okay? Not too bad, right? All right, let's keep going. It is now your turn, okay? Press pause, take a few minutes. Work your way through these problems. When you're ready to check your answers, press play again.

(female narrator) Simplify the following expressions. Number 1: Z to the 30th over Z to the 20th. Number 2: M to the 7th times N to the 8th over M to the third times N to the 5th. Number 3: X to the 18th times Y to the 13th times P to the 4th over X to the 12th times Y to the 9th times P squared. All right, you ready? Let's see how you did. C to the 30th divided by Z to the 20th, that's Z to the 10th for that one. Two: M to the 7th, N to the 8th over M to the 3rd, N to the 5th, was M to the 4th, N to the 3rd. All right? Finally: X to the 18th, Y to the 13th, P to the 4th divided by X to the 12th, Y to the 9th, P squared. You should have got X to the 6th, Y to the 4th, P to the second power. To see how I did these, keep with me. How did I get that first one? Okay, just applied my rule, and subtracted my exponents. So 30 minus 20, that's 10. That means that this will simplify to Z to the 10th. On the next one, I had two different variables, but I applied the exact same process. I handled the Ms first. M to the 7th divided by M to the 3rd, you just subtract your exponents. So 7 minus 3, that's 4. That means the M piece of that simplifies to M to the 4th. Got the first bit. All right, then I have to handle the Ns. I have N to the 8th divided by N to the 5th. Just apply your rule. Subtract the exponents. Okay, 8 minus 5, that's 3, so N to the 3rd. Then you've got the last part of that. That's how I got number 2. If you need to see how I did the last one... This is the one with three different variables. Take them one at a time-- the same type at a time. So X to the 18th over X to the 12th. Just subtract your exponents. 18 minus 12, that's 6, so X to the 6th. That was the first part. Then handle the Ys. So Y to the 13th over Y to the 9th. Subtract your exponents, so 13 minus 9. That's 4, right? That's where the Y to the 4th came from. Then we have the Ps. So P to the 4th divided by P squared. Subtract your exponents. 4 minus 2, that's 2, so P to the 2nd power. That's where the last piece came from. That's how I got those three answers. There's another kind of problem that applies this rule. I want you to know how to do this type, too.

(female narrator) Simplify the following expressions. Number 1: 75A to the 19th, B to the 18th over 50A to the 11th, B to the 10th. Number 2: 30H to the 9th, V to the 11th, T to the 4th over 5H to the 5th, V to the 3rd, T. You ready to see how you did? Let's compare our answers. For the first one, 75A to the 19th, B to the 18th divided by 50A to the 11th, B to the 10th. That was three halves A to the 8th, B to the 8th, or maybe you wrote it as-- maybe you wrote it as this: 3A to the 8th, B to the 8th over 2. Either one would have been fine. All right, the second one, 30H to the 9th, V to the 11th, T to the 4th divided by 5H to the 5th, V to the 3rd, T. You should have got 6H to the 4th, V to the 8th, T to the 3rd. Okay? See how I did these? Then stay with me, I'll work them out. For the first one, I did what we did before. I focused on those coefficients first. I said, "Okay, 75 divided by 50." Those won't divide evenly, okay? Whenever I see numbers 25, 50, 75, 100, I always think quarters to figure out what my factors are. I think like, "75, that's three quarters," right? The factors of 75, 25 times 3. All right? 50, I know I could factor that with 25 times 2, right? When I do that I see my greatest common factor is 25. I cancel out those 25s. So I got the three halves, the 3 over 2. You notice that's an improper fraction. The numerator is larger than the denominator. In elementary school, people really hated that and wanted to make it a mixed number. When you get to Algebra 1, nobody hates it anymore. Leave an improper fraction as an improper fraction, it's fine. It's easier to leave it like that Algebra. I'll leave that as three halves, okay? Now I'll handle the A part. A to the 19th divided by A to the 11th. I subtract my exponents. So 19 minus 11, that's 8. So A to the 8th. And B to the 18th divided by B to the 10th. Subtract my exponents here. 18 minus 10, that's 8, so B to the 8th. You just remember, like I said, sometimes it's written like this, where you're forced to notice everything that's in the numerator. That 3A to the 8th, B to the 8th, with that 2 on the bottom. Both mean the same thing. I like the first way-- that's my habit-- but either one is fine. It's completely up to you. If you see that second one, same exact process: take the coefficients first, and then deal with the rest. So 30 divided by 5, that's 6. That's where my 6 came from in my answer. Then I handled the Hs. So H to the 9th divided by H to the 5th. Use your quotient of powers rule. Subtract the exponents. So 9 minus 5, that's 4. That's where I got the H to the 4th. Then I handled the Vs. So V to the 11th over V to the 3rd. Subtract your exponents. So 11 minus 3, that's 8. That's where the V to the 8th came from. Then the last bit: that T to the 4th divided by T. Remember how, when you don't see an exponent, there's an invisible 1? So let's subtract 4 minus 1. That's 3, so T to the 3rd. That's where the last bit of that came from. All right, guys! I hope you're using your quotient of powers rule to solve your problems, and that using your knowledge of exponents, division, and factors-- it comes together to help you with these kind of problems. Hope to see you soon.

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In this program, students learn to apply the quotient of powers rule for division. This rule allows for subtracting the exponents if the base numbers are the same. Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 28 minutes