7 1 Integer Exponents Lesson Objectives I will

7 -1 Integer Exponents Lesson Objectives: I will be able to … • Evaluate expressions containing zero and integer exponents • Simplify expressions containing zero and integer exponents Language Objective: I will be able to … • Read, write, and listen about vocabulary, key concepts, and examples Holt Algebra 1

7 -1 Integer Exponents You have seen positive exponents. Recall that to simplify 32, use 3 as a factor 2 times: 32 = 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. Power 55 54 53 52 Value 3125 625 125 25 5 5 5 51 50 5– 1 5– 2 5 5 When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5. Holt Algebra 1

7 -1 Integer Exponents Pages 1 – 2 Remember! Base x 4 Exponent Holt Algebra 1

7 -1 Integer Exponents Page 2 Example 1: Cooking Application One cup is 2– 4 gallons. Simplify this expression. gal is equal to Holt Algebra 1

7 -1 Integer Exponents Page 2 Your Turn 1 A sand fly may have a wingspan up to 5– 3 m. Simplify this expression. 5 -3 m is equal to Holt Algebra 1

7 -1 Integer Exponents Page 3 Example 2: Zero and Negative Exponents Simplify. A. 4– 3 B. 70 7º = 1 C. (– 5)– 4 D. – 5– 4 Holt Algebra 1 Any nonzero number raised to the zero power is 1.

7 -1 Integer Exponents Page 4 Example 3: Evaluating Expressions with Zero and Negative Exponents Evaluate the expression for the given values of the variables. – 2 a 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. Holt Algebra 1

7 -1 Integer Exponents Page 4 Your Turn 3 Evaluate the expression for the given values of the variables. for a = – 2 and b = 6 Substitute – 2 for a and 6 for b. Evaluate expressions with exponents. 2 Holt Algebra 1 Write the power in the denominator as a product. Evaluate the powers in the product. Simplify.

7 -1 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. Holt Algebra 1