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6-1 6-1 Integer IntegerExponents Exponents Warm Up Lesson Presentation Lesson Quiz Holt Holt McDougal Algebra 1Algebra Algebra11 Holt McDougal 6-1 Integer Exponents Warm Up Evaluate each expression for the given values of the variables. 1. x3y2 for x = –1 and y = 10 2. for x = 4 and y = (–7) Write each number as a power of the given base. 3. 64; base 4 4. –27; base (–3) Holt McDougal Algebra 1 6-1 Integer Exponents Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. Holt McDougal Algebra 1 6-1 Integer Exponents RECALL: Positive exponents. To simplify 32, use 3 as a factor 2 times: 32 = ??? VOCABULARY EXPONENT Positive exponents 3 BASE Holt McDougal Algebra 1 5 6-1 Integer Exponents ZERO OR NEGATIVE EXPONENTS look for a pattern to figure it out. Power 55 54 53 52 Value 3125 625 125 25 5 50 = 5 =1 5 5 −1 5 Holt McDougal Algebra 1 = 5 51 5–1 5–2 5 When the exponent decreases by one, the value of the power is divided by 5. 5 1 1 = 1 5 5 50 5 −2 = 1 1 1 ÷5= = 2 5 25 5 6-1 Integer Exponents VOCABULARY 1. Zero Exponents – Any nonzero number raised to the zero power is 1. Examples: 30 = 1 (−16)0 = 1 0 = 1 Holt McDougal Algebra 1 6-1 Integer Exponents VOCABULARY 2. Negative Exponents– A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the opposite (postive) exponent. Example: 1 1 = 2 3 9 3−2 = − 1 = Holt McDougal Algebra 1 2−4 1 1 = = 4 2 16 6-1 Integer Exponents Why “nonzero number” in the previous definition? 0 0 = 0 −2 0 = Holt McDougal Algebra 1 1 1 = = 2 0 0 6-1 Integer Exponents Reading Math 2–4 is read “2 to the negative fourth power.” Holt McDougal Algebra 1 6-1 Integer Exponents Example 1: Application One cup is 2–4 gallons. Simplify this expression. gal is equal to Holt McDougal Algebra 1 6-1 Integer Exponents Try this one yourself!!! A sand fly may have a wingspan up to 5–3 m. Simplify this expression. Holt McDougal Algebra 1 6-1 Integer Exponents Simplify. A. 4–3 B. 70 TRY THESE YOURSELF!!! 7º = 1 C. (–5)–4 D. –5–4 E. (–2)–5 Holt McDougal Algebra 1 6-1 Integer Exponents Caution In (–5)–4, the base is negative because the negative sign is inside the parentheses. In –5–4 the base (5) is positive. Holt McDougal Algebra 1 6-1 Integer Exponents Example 2 Evaluate the expression for the given value of the variables. x –2 for x = 4 Substitute 4 for x. Use the definition Holt McDougal Algebra 1 6-1 Integer Exponents Example 3: Try another yourself!!! Simplify the expression for the given values of the variables. –2a0b-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. Simplify the denominator. Simplify. Holt McDougal Algebra 1 6-1 Integer Exponents Try these yourself!!! Evaluate the expression for the given value of the variable. 1.) p–3 for p = 4 2.) Holt McDougal Algebra 1 for a = –2 and b = 6 6-1 Integer Exponents What if you have an expression with a negative exponent in a denominator, such as ? 1 − = *Move the denominator to the top and change the sign **An answer with a negative exponent IS NOT simplified fully Holt McDougal Algebra 1 6-1 Integer Exponents Example 4: Together Simplify. A. 7w–4 Holt McDougal Algebra 1 B. 6-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. C. and Holt McDougal Algebra 1 6-1 Integer Exponents PRACTICE: ON YOUR OWN Simplify. a. 2r0m–3 b. Holt McDougal Algebra 1 c. 6-1 Integer Exponents 6.1 HOMEWORK PG. 395 - 397 #24-42(all), 44-66(evens), 78-83, 100 Holt McDougal Algebra 1