2. In this lesson, we’re going to learn about an important math
operation called exponents
So, you may question, what are exponents?
Well, just like the four main arithmetic operations that we use in math
(-,+,X,/),
exponents are a type of math operation.
They tell us what to DO with numbers.
Ok, but what do they tell us to do?
3. Exponents tell us to take a number and multiply it by itself a certain
number of times. In other words, exponents are basically repeated
multiplication.
24
Yes, that’s an exponent, and in a minute we’ll talk about why it
looks like that and why the numbers are different sizes.
But for now, you just need to know that this exponent tells us to
take the number 2 and multiply it 4 times.
4. In other words, you’d take four ‘2’s and multiply them together.
2 × 2 × 2 × 2 which would equal 16.
So, multiplication shows repeated addition and exponents show
repeated multiplication. And we’ll see more examples of how
exponents work in a minute.
But first, let’s talk a little bit about why exponents look the way
they do.
5. Exponents involve two numbers.
24
The first number is the one that gets multiplied repeatedly a certain
number of times.
First number 24
2X2X2X2
And it’s written full size and it’s called the “base”.
base 24
6. The second number tells us how many copies of the base to multiply together.
2 𝟒
Exponent
It’s written much smaller and up at the top of the line like this. And it’s called
the exponent (or the Index). usually be read, “two to the fourth power”, or just
“two to the fourth” for short.
And when reading exponents, some interesting terminology is used…
And this exponent would be read, “three to the fifth power”, or just “three to
the fifth”.
3 𝟓
And this exponent would be read, ”ten to the sixth power”, or just “ten to the
sixth”.
10 𝟔
7. I know what some of you are thinking.
“Where’s the operator symbol?”
If exponents are math operations, don’t we need a symbol that goes between
them? like there is with multiplication and the other arithmetic operations?
Well, yes and no.
Most of the time, we don’t need a special operation symbol because of the
way the numbers are written. Since the exponent is written smaller and up at
the top of the line, it looks much different from a normal digit, so we don’t
need to use a symbol.
In math, whenever you see a regular sized number with a smaller number up
and to the right, you know it’s an exponent.
8. And once you get used to seeing exponents like this, it’s easy to recognize
them. The only real concern is when writing exponents down on paper
when you’re trying to solve problems. If you’re not careful, or have really
messy handwriting, you might accidentally confuse an exponent (like two
to the fifth) with a two-digit number (like 25) and obviously that would be a
problem.
But even if you’re careful when writing exponents, there are some
times when you really do need a special symbol.
9. like when you type an exponent into a computer.
In that case, it’s very common to use the “carrot” symbol as the exponent
operator.
The carrot symbols looks like this.
( ^ )
So, 2 to the 5th power would be written as “2 ^ 5”,
and 3 to the 4th power would be written as “3 ^ 4”.
10. And that notation is used all the time in computer programing.
Oh, and one more thing you should know before we move on…
is that exponent operations do NOT have the commutative property.
In other words, you can’t switch the order of the numbers, without getting
a different answer.
So exponents do NOT have the commutative property.
11. Okay, now that you know what exponents are, and you know how they’re
written,
it’s time to talk about how they’re used in math.
As I mentioned earlier, exponents are a way of doing repeated
multiplication.
3 𝟐
power is the same as 3 × 3
3 𝟑
is the same as 3 × 3 × 3
3 𝟒
is the same as 3 × 3 × 3 × 3
3 𝟓
is the same as 3 × 3 × 3 × 3 × 3
Do you see the pattern?
12. Okay, so now you know that exponents are a way of showing repeated
multiplication, and you also know what the two numbers in an exponent
mean.
The base is the number that will get repeatedly multiplied together,
and the exponent (or index) tells us how many times to repeat it.
Please, practice the following:
In the next presentation, we’ll learn more about exponents.
Learning math takes a lot of practice, so be sure to practice what you’ve
learned in this presentation.
Thanks for watching this PowerPoint and I’ll see you next time.
