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This video is provided as supplementary material
for courses taught at Howard Community College and
this is going to be an introduction to exponents. So let's get started.
Let's say I have a situation like this
where I've got the number 5 and I want to multiply it by itself
4 times. I want to multiply 5 times 5 times 5 times 5.
Well, I could write it out like this or I could use exponents
and write it in a much simpler manner. Using exponents,
I'm going to write the number 5 and then,
after it and a little bit higher, I'm gonna write a small number 4.
That 4 is
an exponent. The five is called the base of the exponent.
So that's the base and the 4
is the exponent. And what this notation means
is we take the number that's the base, the 5,
and we multiply it repeatedly, in this case four times.
The exponent tells us how many times we're multiplying.
So both of these notations mean the same thing ---
5 times 5 times 5 times 5, and I could multiply that out,
or I could just write 5 with the exponent 4 after it.
Now let's take a couple minute and talk about
how you're going to say this.
Formally, if you've got a situation like this, a base of 5
and an exponent that's 4, you would say
"5 raised to the fourth power." But most people don't say that much.
They may say "5 raised to the fourth"
or "5 the fourth power"
or just "5 to the fourth". All those would mean the same thing.
Now if we're just multiplying something by itself two times,
so in other words 5 raised to the second power,
which of course would be 5 times 5,
you may also hear people
calling this "5-squared." So if the exponent is a 2,
people may just use the term "squared" after it.
instead of saying "5 to the second."
If the exponent is 3,
like 5 to the third power, then instead of "five to the third"
people say "5 cubed".
So when the exponent is a 2, people may say "squared"
instead of five or whatever to the second.
When the exponent is a 3, they may say cubed
instead of five to the third.
So let's just look at some examples and make sure we have a good handle on this.
So here's 2
with the exponent 5. That would be
2-to-the-fifth or 2-raised- to-the-fifth-power, or 2-to-the-fifth power,
and that's just going mean
2 times 2 times 2 times 2
times 2. I'm multiplying 2 repeatedly,
5 times. We could multiply that out...
2 times 2 would be 4, times 2 more would be 8,
times 2 more would be 16, and then times 2 more
would be 32. If I have 3 the fourth power,
that would be the base, 3,
multiplied repeatedly
4 times. I know that from the exponent.
So 3 times 3 would be 9,
times 3 again would be 27, and times 3 again
would be 81.
I've got 7 to the second power,
or 7 squared. That's just 7 times 7,
or 49.
and here I've got 4 to the third power,
or 4 cubed, so that's
4 times 4 times 4.
4 times 4 is 16, times 4 again would be 64.
Okay,
so that's the basic introduction to exponents. Take care,
I'll see you next time.