Grade 8 Module 1 Lesson 1

Module 1 Lesson 1: Exponential Notation

Grade 8 Math

Is there a shorter way to write 3+3+3+3+3?

We can abbreviate the problem 3+3+3+3+3 because we are adding the same number over and over again.

3+3+3+3+3 can be changed from addition into multiplication.

Is there a shorter way to write 3x3x3x3x3?

You can abbreviate a multiplication problem as well, when you are multiplying the same number over and over again.

We use exponents to abbreviate a number that is multiplied a lot of times.

An exponent is written with a small number in the top right corner

The number that you are multiplying (3) is called your base, and the exponent is the number of times you are multiplying your digit.

Here are some more examples of changing an equation from expanded form into exponential form.

Notice that if a repeating base is a fraction or a negative number, it is written in parentheses and the exponent is written on the outside.

Practice problems

You will now begin some practice problems for turning expanded form into exponential form. Use a notebook if you need.

Multiple Choice

 $2\times2\times2\times2\times2\times2$  

•  $2\times6$  

•  $2+6$  

•  $6^2$  

•  $2^6$  

Multiple Choice

 $4\times4\times4\times4\times4\times4\times4$  

•  $4^7$  

•  $7^4$  

•  $4\times7$  

•  $7\times4$  

Multiple Choice

 $\left(\frac{7}{2}\right)\times\left(\frac{7}{2}\right)\times\left(\frac{7}{2}\right)$  

•  $\left(\frac{7}{2}\right)^{\left(\frac{7}{2}\right)}$  

•  $\left(\frac{7}{2}\right)^3$  

•  $\left(\frac{7}{2}\right)+\left(\frac{7}{2}\right)+\left(\frac{7}{2}\right)$  

•  $72^{\left(\frac{7}{2}\right)}$  

Multiple Choice

 $-4\times-4\times-4\times-4\times-4$  

•  $4^5$  

•  $4^{-5}$  

•  $-4^5$  

•  $\left(-4\right)^5$  

Now that you've tried those practice problems, think about this in preparation for next class...

Will the answer to  $\left(-1\right)^{12}$  be positive or negative?

Will the answer to  $\left(-1\right)^{13}$   be positive or negative?