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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.

People are always looking for the easy wayâ€¦ the shortcut. Folks are always wanting something to make their jobs easier. Some people even want their relaxation to be as easy as possible. For example, the TV remote. It's way too difficult to get up and change the channel - we have to be able to do that from a prone position on the couch.

Mathematicians are no different. Any way they can find to write things more simply, to save time and space (and ink in the math books, to be honest), they will do it.

**Exponential notation** is a mathematical shortcut. It is a method for writing an equation that shows a certain term multiplied to itself many times.

The exponent is written as a superscript number after the base number. The exponent tells how many times the base is to be multiplied to itself. In this picture, the base number is the 2 and the exponent is the three. The notation means that 2 is to be multiplied to itself 3 times.

2 x 2 x 2

Exponential notation can also be written with a carat (^), like this:

2^3

Let's try an example of simplifying a multiplication problem with exponential notation.

Say we had this mathematical expression

4 x 4 x 4 x 4 x 4 x 4 x 4 x 4

It's long, hard to understand and easy to get confused. If it could be written simpler, that would be wonderful. This is where exponential notation comes into play. This equation written in exponential notation would be:

48 or 4^8

because there are 8 4s being multiplied to each other.

Here's another example.

Simplify *X* x *X* x *X* x *X* x *X* x *X* x *X* x *X* x *X* x *X* x *X*

When we count the *X*s, we find that there are 11, which means that the exponent will be 11.

The solution is *x*11 or *x*^11.

We can also go the other way.

Write out 3^5.

The exponent tells us that this equation will have 3 multiplied to itself 5 times. So, written out, 3^5 is:

3 x 3 x 3 x 3 x 3

Exponential notation involves writing certain mathematical equations in a simpler form. An expression written with exponential notation will describe how many times (the exponent) to multiply a number (the base) to itself. It is an easier way to write what could be a longer complicated multiplication problem.

After watching this lesson, you should be able to define exponential notation and explain how it is used in mathematics.

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- How to Use Exponential Notation 2:44
- Simplifying and Solving Exponential Expressions 7:27
- Exponential Expressions & The Order of Operations 4:36
- Multiplying Exponential Expressions 4:07
- Dividing Exponential Expressions 4:43
- The Power of Zero: Simplifying Exponential Expressions 5:11
- Negative Exponents: Writing Powers of Fractions and Decimals 3:55
- Power of Powers: Simplifying Exponential Expressions 3:33
- Go to High School Algebra: Exponents and Exponential Expressions

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