In math, we use an exponent as a short way of writing the same number multiplied by itself several times. For example: 34 = 3 × 3 × 3 × 3, or 125 = 12 × 12 × 12 × 12 × 12. The exponent tells you how many times the number (called the base) will be multiplied by itself.

Some numbers, like 2 and 10, make easy-to-solve patterns when repeatedly multiplied. The pattern for repeatedly multiplying by 2, for example, is to just keep doubling the result.

21
22
23
24
25
26
27
2
2 × 2
2 × 2 × 2
2 × 2 × 2 × 2
2 × 2 × 2 × 2 × 2
2 × 2 × 2 × 2 × 2 × 2
2 × 2 × 2 × 2 × 2 × 2 × 2
2
4
8
16
32
64
128

Copy and complete the following table on a separate piece of paper to find the pattern for 10.

101
102
103
104
105
106
107
10
10 × 10
 
10

Click here to see a completed table.

101
102
103
104
105
106
107
10
10 × 10
10 × 10 × 10
10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10
10
100
1,000
10,000
100,000
1,000,000
10,000,000
Close Pop Up

Based on the information in the table, answer the following questions in your notes:

How do the numbers in the bottom row change as you move from left to right?

Check Your Answer

The numbers get bigger. Each time you move one cell to the right, you add a zero on the end of the number. Close Pop Up

How does the number of zeros in the final answer compare to the number of times 10 is used as a factor?

Check Your Answer

The number of zeros in the final answer is the same as the number of times 10 is used as a factor. Close Pop Up

What rule does this suggest for how the number of zeros in the final answer compares to the exponent in the top row?

Check Your Answer

The number of zeros will be the same as the exponent. Close Pop Up

Using your rule, how would you write one billion (1,000,000,000) as 10 raised to an exponent?

Check Your Answer

1,000,000,000 = 109 Close Pop Up

What would happen if you raise 10 to no power? 100 = ?

Check Your Answer

There would be no zeros on the answer. 100 = 1 Close Pop Up