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 |
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10 |
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 |
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?
Interactive popup. Assistance may be required. The numbers get bigger. Each time you move one cell to the right, you add a zero on the end of the number.How does the number of zeros in the final answer compare to the number of times 10 is used as a factor?
Interactive popup. Assistance may be required. The number of zeros in the final answer is the same as the number of times 10 is used as a factor.What rule does this suggest for how the number of zeros in the final answer compares to the exponent in the top row?
Interactive popup. Assistance may be required. The number of zeros will be the same as the exponent.Using your rule, how would you write one billion (1,000,000,000) as 10 raised to an exponent?
Interactive popup. Assistance may be required. 1,000,000,000 = 109What would happen if you raise 10 to no power? 100 = ?
Interactive popup. Assistance may be required. There would be no zeros on the answer. 100 = 1