7 1 Integer Exponents Objectives Evaluate expressions containing

7 -1 Integer Exponents Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. 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 Holt Algebra 1 5 5 5 51 5 50 5– 1 5– 2

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

7 -1 Integer Exponents Holt Algebra 1

7 -1 Integer Exponents Notice the phrase “nonzero number” in the previous table. This is because 00 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. Holt Algebra 1

7 -1 Integer Exponents Reading Math 2– 4 is read “ 2 to the negative fourth power. ” Holt Algebra 1

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

7 -1 Integer Exponents Check It Out! Example 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 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 Caution In (– 3)– 4, the base is negative because the negative sign is inside the parentheses. In – 3– 4 the base (3) is positive. Holt Algebra 1

7 -1 Integer Exponents Simplify. Check It Out! Example 2 a. 10– 4 b. (– 2)– 4 c. (– 2)– 5 d. – 2– 5 Holt Algebra 1

7 -1 Integer Exponents Example 3 A: 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 Holt Algebra 1

7 -1 Integer Exponents Example 3 B: 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 Check It Out! Example 3 a 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. Holt Algebra 1

7 -1 Integer Exponents Check It Out! Example 3 b 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. An ifexpression that contains exponent negative or zero So a base with a negative is in a exponents is not denominator, it is considered equivalent to to be thesimplified. same base with Expressions be exponent rewritten with positive the opposite should (positive) in theonly numerator. exponents. Holt Algebra 1

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

7 -1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. C. and Holt Algebra 1

7 -1 Integer Exponents Check It Out! Example 4 Simplify. a. 2 r 0 m– 3 rº = 1 and b. Holt Algebra 1 c. .

7 -1 Integer Exponents Lesson Quiz: Part I 1. A square foot is 3– 2 square yards. Simplify this expression. Simplify. 2. 2– 6 3. (– 7)– 3 4. 60 5. – 112 Holt Algebra 1 1 – 121

7 -1 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. Holt Algebra 1 for a = 6 and b = 3