Exponents Lesson

Learn about the rules of exponents with the following examples and interactive exercises.

In the table below, the number 2 is written as a factor repeatedly. The product of factors is also displayed in this table. Suppose that your teacher asked you to Write 2 as a factor one million times for homework. How long do you think that would take? Answer.

Writing 2 as a factor one million times would be a very time-consuming and tedious task. A better way to approach this is to use exponents. Exponential notation is an easier way to write a number as a product of many factors.

Base^Exponent

The exponent tells us how many times the base is used as a factor.

For example, to write 2 as a factor one million times, the base is 2, and the exponent is 1,000,000. We write this number in exponential form as follows:

2^1,000,000 

read as two raised to the millionth power

Example 1: Write 2 x 2 x 2 x 2 x 2 using exponents, then read your answer aloud.

Solution: 2 x 2 x 2 x 2 x 2  =  2⁵             2 raised to the fifth power

Let us take another look at the table from above to see how exponents work.

So far we have only examined numbers with a base of 2. Let’s look at some examples of writing exponents where the base is a number other than 2.

Example 2: Write 3 x 3 x 3 x 3 using exponents, then read your answer aloud.

Solution: 3 x 3 x 3 x 3  =  3⁴           3 raised to the fourth power

Example 3: Write 6 x 6 x 6 x 6 x 6 using exponents, then read your answer aloud.

Solution: 6 x 6 x 6 x 6 x 6  =  6⁵           6 raised to the fifth power

Example 4: Write 8 x 8 x 8 x 8 x 8 x 8 x 8 using exponents, then read your answer aloud.

Solution: 8 x 8 x 8 x 8 x 8 x 8 x 8  =  8⁷           8 raised to the seventh power

Example 5: Write 10³, 3⁶, and 1⁸ in factor form and in standard form.

Solution: 

The following rules apply to numbers with exponents of  0, 1, 2 and 3:

Summary: Whole numbers can be expressed in standard form, in factor form and in exponential form. Exponential notation makes it easier to write a number as a factor repeatedly. A number written in exponential form is a base raised to an exponent. The exponent tells us how many times the base is used as a factor.

Exercises

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. Do not use commas in your answers, just digits. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.