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Let's go through some more exponent examples.

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

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

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

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

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

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

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And then we multiply them.

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And we will get, let's see –

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

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

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

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

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You will get the exact same result here.

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So let's do one more example like that.

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

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

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

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

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

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

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

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

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