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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 more
exponent examples. So to warm up, let's think
about taking a fraction to some power. So let's say I have
2/3, and I want to raise it to the
third power here. Now, 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 2/3, two
2/3's, and three 2/3's. So that's one, two, three, 2/3. And then we multiply them. And we will get-- let's
see, the numerator will be 2 times 2
times 2, which is 8. And the denominator's
going to be 3 times 3 times 3 times 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, raising something
to the third power, people sometimes say,
you're cubing it. But let's raise 4/9
to the second power. Let's square it. And 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 times 4, which is 16. And your denominator
is going to be 9 times 9, which is equal to 81.