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### Course: Algebra basics > Unit 1

Lesson 3: Exponents- Intro to exponents
- Exponent example 1
- Exponent example 2
- Squaring numbers
- Intro to exponents
- The 0 & 1st power
- Powers of zero
- Meaning of exponents
- 1 and -1 to different powers
- Comparing exponent expressions
- Exponents of decimals
- Powers of whole numbers
- Evaluating exponent expressions with variables
- Variable expressions with exponents
- Exponents review

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# Intro to exponents

Exponents represent repeated multiplication, making numbers grow quickly. For example, 2 to the 3rd power means multiplying three 2's together, resulting in 8. This concept differs from multiplication, which is simply repeated addition. Understanding exponents is essential for mastering higher-level math. Created by Sal Khan.

## Want to join the conversation?

- can you have an exponent that has a decimal or fraction like 5^4.8?(77 votes)
- Yes, it's like this:
*4.8 = 4 4/5 = 24/5. So it's 5 √5 to the power of 24*.**So the answer is 1**.(10 votes)

- What happens when an exponent is negative?

I don't really understand.

Please help me!!(17 votes)- leilaizarte, when you have a positive exponent, you are multiplying the base number by itself for as many times as the exponent indicates. For example, 10^3 is the same as 10 x 10 x 10, or 1000. Similarly, a negative exponent indicates how many times you must divide by that number. For example, 10^-3 is the same as 1 ÷ 10 ÷ 10 ÷ 10, or .001.(29 votes)

- So are Exponents like repeated multiplication?(0:22-0:30)(15 votes)
- yes you are correct(9 votes)

- (1:44) What are powers? I'm really confused...(6 votes)
- Its just another name for exponents for example 4^4 is said as four to the fourth power.(19 votes)

- I understand the smaller exponents but what about large ones such as 9^33 could you say 33^9 and it be the same awnser?(7 votes)
- 9^33 is going to be larger. Try it in a calculator :o

Exponentiation is not like multiplication in that you can swap the numbers and get the same answer. Exponentiation is not commutative.(8 votes)

- what is 23 to the 42 power(4 votes)
**1.558006e+57**thats the answer to your question!(8 votes)

- How do I divide exsponents I don't get it(3 votes)
- To divide exponents with the same base, keep the base and subtract the exponents:

3^5 / 3^3

5 - 3 = 2 (This is our new exponent)

Answer: 3^2(9 votes)

- when your multiplying like 2 x 2 x 2 do u always have to put the dot for multiplication in that situation?(5 votes)
- In algebra, there are many different symbols, and if you write like 2 x 2 x 2, people will think it it is variable if you write it down like that. If you are not doing algebra, you could do that, but it is not ideal.

Thanks(4 votes)

- Can I do any number to the power of a negative number?

Like, 3^ -2 ??(3 votes)- You can do any number except 0 to a negative power. The reason is that 0 to a negative power would be division by 0 which is undefined.(6 votes)

- why doesn't 2 3 and 3 2 don't have the same answer.(5 votes)
- A unique property of exponentiation is that despite being like repeated multiplication (which is commutative), it is not like multiplication in that you can swap the numbers and get the same answer. Exponentiation is not commutative.

In your case, 2^3 =/= 3^2, showing this property.(4 votes)

## Video transcript

You already know that we can view multiplication as repeated addition. So, if we had 2 times 3 (2 × 3), we could literally view this as 3 2's being added together. So it could be 2 + 2 + 2. Notice this is [COUNTING: 1, 2] 3 2's. And when you add those 2's together, you get 6. What we're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication. And that's the operation of taking an 'exponent.' And it sounds very fancy. But we'll see with a few examples that it's not too bad. So now, let's take the idea of 2 to the 3rd power (2^3) – which is how we would say this. (So let me write this down in the appropriate colors.) So 2 to the 3rd power. (2^3.) So you might be tempted to say, "Hey, maybe this is 2 × 3, which would be 6." But remember, I just said this is repeated multiplication. So if I have 2 to the 3rd power, (2^3), this literally means multiplying 3 2's together. So this would be equal to, not 2 + 2 + 2, but 2 × ... (And I’ll use a little dot to signify multiplication.) ... 2 × 2 × 2. Well, what's 2 × 2 × 2? Well that is equal to 8. (2 × 2 × 2 = 8.) So 2 to the 3rd power is equal to 8. (2^3 = 8.) Let's try a few more examples here. What is 3 to the 2nd power (3^2) going to be equal to? And I'll let you think about that for a second. I encourage you to pause the video. So let's think it through. This literally means multiplying 2 3's. So let's multiply 3 – (Let me do that in yellow.) Let's multiply 3 × 3. So this is going to be equal to 9. Let’s do a few more examples. What is, say, 5 to the – let's say – 5 to the 4th power (5^4)? And what you'll see here is this number is going to get large very, very, very fast. So 5 to the 4th power (5^4) is going to be equal to multiplying 4 5's together. So 5^4 = 5 × 5 × 5 × 5. Notice, we have [COUNTING: 1, 2, 3] 4 5's. And we are multiplying them. We are not adding them. This is not 5 × 4. This is not 20. This is 5 × 5 × 5 × 5. So what is this going to be? Well 5 × 5 is 25. (5 × 5 = 25.) 25 × 5 is 125. (25 × 5 = 125.) 125 × 5 is 625. (125 × 5 = 625.)