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§ 1.6 Properties of Integral Exponents

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**Blitzer, Intermediate Algebra, 5e – Slide #2 Section 1.6**

Properties of Exponents Exponent Rules Product Rule Quotient Rule When multiplying exponential expressions with the same base, add the exponents. When dividing exponential expressions with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 1.6

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**Blitzer, Intermediate Algebra, 5e – Slide #3 Section 1.6**

Properties of Exponents Exponent Rules Examples Product Rule Quotient Rule Blitzer, Intermediate Algebra, 5e – Slide #3 Section 1.6

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**Blitzer, Intermediate Algebra, 5e – Slide #4 Section 1.6**

Properties of Exponents The Zero Exponent Rule: If b is any real number other than 0, then Negative Exponent Rule: If b is any real number other than 0 and n is a natural number, then and Blitzer, Intermediate Algebra, 5e – Slide #4 Section 1.6

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**Properties of Exponents**

Exponent Rules Examples Zero Exponent Rule Negative Exponent Rule Blitzer, Intermediate Algebra, 5e – Slide #5 Section 1.6

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**Properties of Exponents**

Exponent Rules Examples Negative Exponents in Numerators and Denominators Power Rule Blitzer, Intermediate Algebra, 5e – Slide #6 Section 1.6

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**Blitzer, Intermediate Algebra, 5e – Slide #7 Section 1.6**

Properties of Exponents Exponent Rules Examples Products to Powers Quotients to Powers Blitzer, Intermediate Algebra, 5e – Slide #7 Section 1.6

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**Simplification Techniques**

Simplifying Exponential Expressions Simplification Techniques Examples If necessary, remove parentheses by using the Products to Powers Rule or the Quotient to Powers Rule. If necessary, simplify powers to powers by using the Power Rule. Blitzer, Intermediate Algebra, 5e – Slide #8 Section 1.6

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**Simplification Techniques**

Simplifying Exponential Expressions Simplification Techniques Examples Be sure each base appears only once in the final form by using the Product Rule or Quotient Rule If necessary, rewrite exponential expressions with zero powers as 1. Furthermore, write the answer with positive exponents by using the Negative Exponent Rule Blitzer, Intermediate Algebra, 5e – Slide #9 Section 1.6

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**Blitzer, Intermediate Algebra, 5e – Slide #10 Section 1.6**

Properties of Exponents Of I M P O R T A N CE to note… Be sure you pay special attention to the study tip on the bottom of page 72. This tip will help you avoid common errors that can occur when simplifying exponential expressions. Blitzer, Intermediate Algebra, 5e – Slide #10 Section 1.6

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