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.