Powers of fractions

Let's go through some more exponent examples.

So to warm up, let's think about
taking a fraction to some power.

So let's say I have two-thirds (2/3), and
I want to raise it to the 3rd power here.

And we've already learned there are
two ways of thinking about this.

One way is to say let's take three 2/3's –

So that's one 2/3rd, two 2/3's, and three 2/3's.

So that's (COUNTING: One, two) three 2/3's.

And then we multiply them.

And we will get, let's see –

The numerator will be 2 × 2 × 2, which is 8.

And the denominator's going to be
3 × 3 × 3, which is equal to 27.

Now the other way of viewing this is you start
with a 1 and you multiply it by 2/3 three times.

So you multiply by 2/3 once, twice, three times.

You will get the exact same result here.

So let's do one more example like that.

So lets say I had 4/9, and I want to square it.

When I raise something to the second power,
people often say, "You're squaring it."

Also when you're raising something to the 3rd power,
people sometimes say, "You're cubing it."

But let's raise 4/9 to the 2nd power.
Let's square it.

I encourage you to pause the video
and work this out yourself.

Well, once again, you could view this as
taking two 4/9's and multiplying them.

Or you could view this as starting with a 1,
and multiplying it by 4/9 two times.

Either way, your numerator is
going to be 4 × 4, which is 16.

And your denominator is going
to be 9 × 9, which is equal to 81.