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

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is get some practice evaluating
exponents of decimals.

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

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Pause this video, see
if you can figure out

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what that is going to be.

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Well, this would just mean
that if I take something

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

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and I multiply them together.

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So it's 0.2 times 0.2 times 0.2.

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Well, what is this going to be equal to?

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

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

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and then I have one
number behind the decimal

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to the right of the decimal here.

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I have another digit to
the right of the decimal

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

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

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And then if I were to
multiply that times 0.2,

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so if I were to multiply that together

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what is that going to be equal to?

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Well, four times two is equal to eight

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and now I have one, two, three numbers

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to the right of the decimal point,

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

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to the right of the decimal point.

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

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let's do another example.

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

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

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

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And what's that going to be equal to?

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Well, you could just say nine times nine

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

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in the two numbers that I'm multiplying

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

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to the right of the decimal point

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

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to the right of the decimal point.

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So put the decimal right over there

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and I'll put the zero, so 0.81.

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

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is 81 hundredths, but there you go.

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Using exponents, or taking
exponents of decimals

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

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It's just in this case you just have to

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do a little bit of decimal multiplication.