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
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22
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23
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24
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25
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26
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27
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2
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2 × 2
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2 × 2 × 2
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2 × 2 × 2 × 2
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2 × 2 × 2 × 2 × 2
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2 × 2 × 2 × 2 × 2 × 2
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2 × 2 × 2 × 2 × 2 × 2 × 2
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2
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4
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8
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16
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32
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64
|
128
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Copy and complete the following table on a separate piece of paper to find the pattern for 10.
101
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102
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103
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104
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105
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106
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107
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10
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10 × 10
|
|
|
|
|
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10
|
|
|
|
|
|
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Click here to see a completed table.
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?
- How does the number of zeros in the final answer compare to 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?
- Using your rule, how would you write one billion (1,000,000,000) as 10 raised to an exponent?
- What would happen if you raise 10 to no power? 100 = ?