40 lines
1.3 KiB
Markdown
40 lines
1.3 KiB
Markdown
---
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title: Exponents
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---
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## Exponents
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An exponent is shorthand for the number of times a number is multipled by itself. It is typically denoted with a superscript, karat, or with "to the power of" such as:
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- 2<sup>3</sup>
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- 2^3
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- 2 to the power of 3
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In this example, 3 is the exponent.
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To compute the value of 2<sup>3</sup>, you would multiply 2 to itself 3 times: 2 * 2 * 2. This evaluates to 8.
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The general format of writing an exponent is:
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- base<sup># of times you multiply base by itself</sup>
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Common exponents have special names:
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- An exponent of 2 means the number is squared. So 3<sup>2</sup> is referred to as 3 squared, evaluating to 9.
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- An exponent of 3 means the number is cubed. So 2<sup>3</sup> is referred to as 2 cubed, evaluating to 8.
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### Negative Exponents
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Negative exponents are computed similarly, except the value is placed as a denominator beneath a numerator of 1.
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For example, 2<sup>-2</sup> = <sup>1</sup>/<sub>(2 * 2)</sub> = <sup>1</sup>/<sub>4</sub>
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### More Examples
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2<sup>5</sup> = 2 * 2 * 2 * 2 * 2 = 32
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(-2)<sup>5</sup> = -2 * -2 * -2 * -2 * -2 = -32
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10<sup>6</sup> = 1,000,000
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2<sup>-5</sup> = <sup>1</sup>/<sub>(2 * 2 * 2 * 2 * 2)</sub> = <sup>1</sup>/<sub>32</sub>
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### More Information:
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- [Wikipedia](https://en.wikipedia.org/wiki/Exponentiation)
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