Exponent Rules Project
Storyboard Text
- Hello Mr. Smith. Thanks for coming today. I have some questions about exponent rules I want to ask you about. Before we begin, enjoy the food.
- Welcome to our Food Festival and Math Spectacle
- Of course. The food sounds delicious. Now, what questions do you want to ask?
- Well to begin with, I don't really understand what exactly the base and exponent is.
- Definition of Base and Exponent
- To visualize it, we'll use 3^2 as an example. Here, 3 is the base and 2 is the exponent.
- The base is the number that's being multiplied and the exponent signifies how many times the number multiplies itself by.
- Ok, I think I understand it more. Can variables and terms also be bases for exponents?
- Alright, I understand it now.
- These bases are just some simple examples. They can get much more complex.
- Yes, terms and variables can also be bases. For example, common variables used are x and y. Terms like (x+3) may also be used.
- I feel like I've heard of them before but I'm not sure what they are. Could you explain?
- Product Rule
- The product rule states that when multiplying 2 bases with the same exponents, the exponents are added together. For example, x^2 * x^3 would equal to x^5.
- Since we're on the topic of exponents and bases, we should go over the product and quotient rule.
- Like what?
- Wow, that sounds like a lot.
- Don't worry. You'll be able to remember them with some practice. Let me start with the power to power rule.
- The most important rules you have to remember are the power to power, zero exponent, and negative exponent rule.
- There are some other rules that you must remember as well when it comes to exponents.
- Then, what's the quotient rule?
- Do negative exponents apply?
- Quotient Rule
- It states that when dividing two bases with the same exponents, the exponents are subtracted from each other. For example, x^7/ x^2 would equal to x^5.
- Yes, negative exponents work the same. For example x^2 * x^-4 would equal to x^-2 and x^3/ x^-4 would equal to x^7.
- The quotient rule is very similar to the exponent rule except that it has to do with division.
- So, since we multiply the exponents of (y^2)^3 together, we should get y^6. As for (y^2)^-3, we would get y^-6.
- So like, if have (y^2)^3 or (y^2)^-3 then we multiply, the exponents together.
- Power to Power Rule
- Yes, exactly.
- The power to power rule states that when a base with an exponent is raised to another exponent, the exponents multiply. Negatives also apply
- What's that. Sounds a little complicated.
- Anything? So, numbers, variables, and terms all apply. Then something like 3^0 or even (3x^3*6^-2)^0 would both result in 1.
- Zero Exponent Rule
- Yes, however you must also remember that 0 is the only number that you can't raise to the power of 0. Anything else is fine. Let's move on the final rule.
- Actually, it's pretty simple compared to the other rules. All that the rule states is that anything with an exponent of 0 automatically becomes a 1.
- You seemed to pick up on that pretty quickly. Let's move on to the zero exponent rule.
- Could you explain that a little more?
- So, that should work the other way. Then if we have 1/2^-2, it should turn into 2^2.
- Negative Exponent Rule
- Sure, I think it's best to use an example. 2^-2 would become 1/2^2. As you can see, it flips from being either on the numerator to the denominator side.
- Yes, exactly. Just remember that like the zero exponent rule, 0 is the only exception. 0 can't be raised to any negative exponent.
- The last rule is the negative exponent rule. This one is a more complex. It states that when we have a negative exponent we flip it over the fraction line and turn it positive.
- Really? Thanks!
- Since I'm already here and you picked up the previous concepts pretty quickly, I'll go over some other stuff you should know.
- That already sounds difficult.
- So, based off what I see, the exponent becomes the numerator and the index becomes the denominator.
- How to Convert from Radical Notation to Exponential Notation
- Yes, what you're saying is correct. The same also applies to stuff like (√2)^3. The index would still become the denominator and the exponent the numerator.
- Don't worry. It's basically another way of displaying square roots. Using an example would be best to explain. Here, we have √(2)^3. This would equal to 2^3/2. To elaborate. we turn it into fraction form.
- I'll start with something simple. How to convert from radical to exponential notation.
- That wasn't so bad actually.
- That should be similar to converting from radical to exponential notation, right?
- Wait! Let me try it out. x^5/2 would become √x^5. The numerator goes back to being the exponent and the radical the index.
- How to Convert from Exponential to Radical Notation
- Not exactly. But since you've already learned that, this should be easier to understand. Basically, the reverse -
- Yes, you're right. Good job.
- Exactly. I might as well explain how to convert from exponential to radical notation.
- That shouldn't be too difficult. Right?
- That's all? Doesn't sound too bad. So for example, x^2 * y^2 would equal to (x*y)^2 and x^4/y^2 would equal to (x/y)^2.
- When the Bases are Different but the Exponents are the Same
- It shouldn't be too difficult. Afterall, only multiplication and division applies to this. When the bases are different but the exponents the same, you just multiply or divide the numbers and attach the exponents.
- Yep, you're right. Well, that's everything you need to know. Remember to practice your knowledge on this during your free time.
- Finally, we'll go over what happens when the bases are different but the exponents are the same.
- Thanks for helping me. I'll make sure to practice what I've learned. See you on Monday!
- No problem. I think I'll stay here to eat this watermelon. See you on Monday.
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