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.