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32 Integer Exponents Warm Up Evaluate each expression for the given values of the variables. 1. x 3 y 2 for x = –1 and y = 10 2. for x = 4 and y = (–7) Write each number as a power of the given base. –100 4343 3. 64; base 4 (–3) 3 4. –27; base (–3)

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32 Integer Exponents Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. Learning Targets

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32 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. 3125 625 125255 5 5 Power Value 5 5454 5353 5252 5151 5 –1 5050 5 –2 5 5 5 5 5 5

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32 Integer Exponents

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32 Integer Exponents https://www.khanacademy.org/math/arit hmetic/exponents-radicals/negative- exponents-tutorial/v/zero--negative-- and-fractional-exponents

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32 Integer Exponents Zero and Negative Exponents Simplify. A. 4 –3 B. y 0 yº = 1 C. (–5) –4 D. –5 –4

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32 Integer Exponents http://my.hrw.com/math11/math06_07/nsmed ia/lesson_videos/alg1/player.html?contentSrc= 7719/7719.xml

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32 Integer Exponents On Your Own Simplify. a. 10 –4 b. (–2) –4 c. (–2) –5 d. –2 –5

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32 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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32 Integer Exponents Simplify. Example 1: Simplifying Expressions with Zero and Negative Numbers A. 7w –4 B.

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32 Integer Exponents Simplify. C. and

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32 Integer Exponents http://my.hrw.com/math11/math06_07/nsme dia/lesson_videos/alg1/player.html?contentSrc =7721/7721.xml

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32 Integer Exponents On your own Example 1 Simplify. a. 2r 0 m –3 b. c.

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32 Integer Exponents Example 2: 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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32 Integer 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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32 Integer Exponents http://my.hrw.com/math11/math06_07/nsme dia/lesson_videos/alg1/player.html?contentSrc =7720/7720.xml

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32 Integer Exponents On your own! Example 2 Evaluate the expression for the given value of the variable. 3b -3 b b = -3

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32 Integer Exponents On your own! Example 2 Evaluate the expression for the given values of the variables. for a = –2 and b = 6

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32 Integer Exponents

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32 Integer Exponents https://www.khanacademy.org/math/arithm etic/exponents-radicals/exponent- properties/v/exponent-properties-involving- quotients

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32 Integer Exponents Simplify. Example 3: Finding Quotients of Powers A.B.

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32 Integer Exponents C. Simplify. D.

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32 Integer Exponents http://my.hrw.com/math11/math06_07/nsme dia/lesson_videos/alg1/player.html?contentSrc =6360/6360.xml

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32 Integer Exponents Check It Out! Example 1 Simplify. c.d.

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