Introduction to exponents

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.)