Comparing exponent expressions

- [Instructor] So we are asked to order

the expressions from least to greatest

and this is from the
exercises on Khan Academy

and if we're doing it on Kahn Academy,

we would drag these little tiles around

from least to greatest, least on the left,

greatest on the right.

I can't drag it around 'cause this

is just a picture, so
I'm gonna evaluate each

of these, and then I'm gonna rewrite them

from least to greatest.

So let's start with two to the third minus

two to the first.

What is that going to be?

Two to the third minus two to the first.

And if you feel really confident,

just pause this video and try

to figure out the whole thing.

Order them from least to greatest.

Well two to the third, that
is two times two times two,

and then two to the first,
well that's just two.

So two times two is
four, times two is eight,

minus two, this is going
to be equal to six.

So this expression right over here could

be evaluated as being equal to six.

Now, what about this right over here?

What is this equal to?

Well let's see, we have two squared

plus three to the zero.

Two squared is two times two and anything

to the zero power is
going to be equal to one.

It's an interesting thing to think

about what zero to the zeroth power should

be but that'll be a
topic for another video.

But here we have three
to the zeroth power,

which is clearly equal to one.

And so we have two times two plus one.

This is four plus one,
which is equal to five.

So the second tile is equal to five.

And then three squared,
well three squared,

that's just three times three.

Three times three is equal to nine.

So if I were to order them from least

to greatest, the smallest of these

is two squared plus three
to the zeroth power.

That one is equal to five,
so I'd put that on the left.

Then we have this thing that's equal

to six, two to the third power
minus two to the first power.

And then the largest value
here is three squared.

So we would put that tile, three squared.

We will put that tile on
the right, and we're done.