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Holt Algebra Integer Exponents 7-1 Integer Exponents Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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Holt Algebra Integer Exponents Warm Up Evaluate each expression for the given values of the variables. 1. x 3 y 2 for x = –1 and y = for x = 4 and y = (–7) Write each number as a power of the given base. – ; base 4 (–3) 3 4. –27; base (–3)

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Holt Algebra Integer Exponents Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. Objectives

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Holt Algebra Integer Exponents You have seen positive exponents. Recall that to simplify 3 2, use 3 as a factor 2 times: 3 2 = 3 3 = 9. But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out 5 5 Power Value – –2 5 5 5 5 5 5

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Holt Algebra Integer Exponents When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

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Holt Algebra Integer Exponents Base x Exponent Remember! 4

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Holt Algebra Integer Exponents

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Holt Algebra Integer Exponents Notice the phrase “nonzero number” in the previous table. This is because 0 0 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above the table with a base of 0 instead of 5, you would get 0º =. Also 0 –6 would be =. Since division by 0 is undefined, neither value exists.

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Holt Algebra Integer Exponents 2 –4 is read “2 to the negative fourth power.” Reading Math

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Holt Algebra Integer Exponents Example 1: Application One cup is 2 –4 gallons. Simplify this expression. cup is equal to

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Holt Algebra Integer Exponents Check It Out! Example 1 A sand fly may have a wingspan up to 5 –3 m. Simplify this expression m is equal to

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Holt Algebra Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4 –3 B º = 1 Any nonzero number raised to the zero power is 1. C. (–5) –4 D. –5 –4

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Holt Algebra Integer Exponents In (–3) –4, the base is negative because the negative sign is inside the parentheses. In –3 –4 the base (3) is positive. Caution

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Holt Algebra Integer Exponents Check It Out! Example 2 Simplify. a. 10 –4 b. (–2) –4 c. (–2) –5 d. –2 –5

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Holt Algebra Integer Exponents Example 3A: Evaluating Expressions with Zero and Negative Exponents Evaluate the expression for the given value of the variables. x –2 for x = 4 Substitute 4 for x. Use the definition

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Holt Algebra Integer Exponents Example 3B: Evaluating Expressions with Zero and Negative Exponents Evaluate the expression for the given values of the variables. –2a 0 b -4 for a = 5 and b = –3 Substitute 5 for a and –3 for b. Evaluate expressions with exponents. Write the power in the denominator as a product. Evaluate the powers in the product. Simplify.

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Holt Algebra Integer Exponents Check It Out! Example 3a Evaluate the expression for the given value of the variable. p –3 for p = 4 Substitute 4 for p. Evaluate exponent. Write the power in the denominator as a product. Evaluate the powers in the product.

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Holt Algebra Integer Exponents Check It Out! Example 3b Evaluate the expression for the given values of the variables. for a = –2 and b = 6 2 Substitute –2 for a and 6 for b. Evaluate expressions with exponents. Write the power in the denominator as a product. Evaluate the powers in the product. Simplify.

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Holt Algebra Integer Exponents What if you have an expression with a negative exponent in a denominator, such as ? or Definition of a negative exponent. Substitute –8 for n. Simplify the exponent on the right side. So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator. An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents.

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Holt Algebra Integer Exponents Simplify. Example 4: Simplifying Expressions with Zero and Negative Numbers A. 7w –4 B.

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Holt Algebra Integer Exponents Simplify. Example 4: Simplifying Expressions with Zero and Negative Numbers C. and

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Holt Algebra Integer Exponents Check It Out! Example 4 Simplify. a. 2r 0 m –3 b. c. rº = 1 and.

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Holt Algebra Integer Exponents Lesson Quiz: Part I 1. A square foot is 3 –2 square yards. Simplify this expression. Simplify –6 3. (–7) – – –121

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Holt Algebra Integer Exponents Lesson Quiz: Part II Evaluate each expression for the given value(s) of the variables(s). 6. x –4 for x =10 7. for a = 6 and b = 3

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