About this video
Multiplication is repeated addition, and an exponent is repeated multiplication. The video shows that 2^3 means 2 x 2 x 2 = 8 (not 2 x 3 = 6), 3^2 = 3 x 3 = 9, and 5^4 = 5 x 5 x 5 x 5 = 625 (not 5 x 4 = 20).
You'll be able to
- explain that an exponent means repeated multiplication.
- write a power like 5^4 as a product of equal factors.
- work out small powers such as 2^3, 3^2 and 5^4.
Key words
- exponent
- The small raised number that tells how many times to multiply the base by itself.
- power
- A number written with an exponent, like 2 to the 3rd power (2^3).
- repeated addition
- Adding the same number again and again; 2 x 3 = 2 + 2 + 2.
- repeated multiplication
- Multiplying the same number again and again; 2^3 = 2 x 2 x 2.
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.)
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