Sometimes, we have to multiply the same number several times. We can say that we are multiplying the number by itself in this case.
When we have a situation like this, it is helpful to use a little number to show how many times to multiply the number by itself. That little number is called an exponent.
If we were going to write
Using exponents has an even fancier name too. We can say that we use exponential notation when we express multiplication in terms of exponents.
We can use exponential notation to write an expanded multiplication problem into a form with an exponent, we write
We can work the other way around too. We can write a number with an exponent as a long multiplication problem and this is called expanded form.
The base is the number being multiplied by itself in this case the base is 4.
The exponent tells how many times to multiply the base by itself in this case, it is a 3.
Using an exponent can also be called “raising to a power.” The exponent represents the power.
Write the following in exponential notation:
Exponential Notation means to write this as a base with an exponent.
Six times itself four times
This is our answer.
Write the following in expanded form:
Expanded form means to write this out as a multiplication problem.
This is our answer.
We can also evaluate expressions with variables.
Our first step is to write it out into expanded form.
Our answer is 64.
Now it's time for you to try a few on your own.
Write the following in exponential form:
Write the following in expanded form and evaluate the expression:
- a little number that tells you how many times to multiply the base by itself.
- the big number in a variable expression with an exponent.
- Exponential Notation
- writing long multiplication using a base and an exponent
- Expanded Form
- taking a base and an exponent and writing it out as a long multiplication problem.
Here is one for you to try on your own.
To evaluate this expression write it out in expanded form.
Now multiply each part of the expression.
Our answer is 24.
Here is a video for review.
Directions: Name the base and exponent in the following examples. Then write each in expanded form.