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# Powers of fractions

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.