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# Powers of fractions

Just like whole numbers with exponents, fractions are repeatedly multiplied. If you know how to multiply fractions, you're over half way there. Created by Sal Khan.

Video transcript

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.