Exponents of decimals

- [Instructor] What we're
going to do in this video

is get some practice evaluating
exponents of decimals.

So let's say that I have
0.2 to the third power.

Pause this video, see
if you can figure out

what that is going to be.

Well, this would just mean
that if I take something

to the third power, that means
I take three of that number

and I multiply them together.

So it's 0.2 times 0.2 times 0.2.

Well, what is this going to be equal to?

Well, if I take 0.2 times
0.2, that is going to be 0.04.

One way to think about
it, two times two is four

and then I have one
number behind the decimal

to the right of the decimal here.

I have another digit to
the right of the decimal

right over here, so my product
is going to have two digits

to the right of the
decimal, so it'd be 0.04.

And then if I were to
multiply that times 0.2,

so if I were to multiply that together

what is that going to be equal to?

Well, four times two is equal to eight

and now I have one, two, three numbers

to the right of the decimal point,

so my product is going to
have one, two, three numbers

to the right of the decimal point.

So now that we've had a little
bit of practice with that,

let's do another example.

So let's say that I were to
ask you, what is 0.9 squared?

Pause this video and see
if you can figure that out.

All right, well this is just
going to be 0.9 times 0.9.

And what's that going to be equal to?

Well, you could just say nine times nine

is going to be equal to
81, and so, let's see,

in the two numbers that I'm multiplying

I have a total of one, two
numbers, or two digits,

to the right of the decimal point

so my answer's going
to have one, two digits

to the right of the decimal point.

So put the decimal right over there

and I'll put the zero, so 0.81.

Another way to think about it
is nine-tenths of nine-tenths

is 81 hundredths, but there you go.

Using exponents, or taking
exponents of decimals

is the same as when we're
taking it of integers.

It's just in this case you just have to

do a little bit of decimal multiplication.