Exponent of Zero and Negative Exponents.pdf - Lesson 2...

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Lesson 2 Exponent of Zero and Negative Exponents 1 When an exponent 𝑛 is a positive integer, such as 1, 2, 3, 4, … , exponential notation represents the product of repeated factors (the base times itself some number of times) o ? 2 = ? ∙ ? the exponent of 2 indicates there are 2 factors of ? o ? 5 = ? ∙ ? ∙ ? ∙ ? ∙ ? the exponent of 5 indicates there are 5 factors of ? o ? 𝑛 = ? ∙ ? ∙ … ∙ ? the exponent of 𝑛 indicates there are 𝑛 factors of ? What about when an exponent 𝑛 is not a positive integer? In this section we’ll look at exponents of zero and exponents that are negative integers. One way to approach exponents of zero is to think about a term divided by itself; for instance, ? 2 ? 2 = 1 because anything over itself is one. However, what happens if we simplified ? 2 ? 2 using the Quotient Rule that was discussed earlier? ? 2 ? 2 = ? 2−2 = ? 0 This shows that ? 2 ? 2 = ? 0 , and since we already know that ? 2 ? 2 = 1 , that means ? 0 must equal 1 . This leads us to the Zero-Exponent Rule.

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