6 1 Integer Exponents Warm Up Lesson Presentation

6 -1 Integer. Exponents Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Algebra 1 Algebra 11 Holt Mc. Dougal

6 -1 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 Write each number as a power of the given base. 2. 3; base 4 Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Essential Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. Holt Mc. Dougal Algebra 1

6 -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 Mc. Dougal Algebra 1 5 5 5 51 5 50 5– 1 5– 2

6 -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. What’s more? ? ? 1. 2. 3. 4. Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Remember! Base x 4 Exponent Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Reading Math 2– 4 is read “ 2 to the negative fourth power. ” Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Example: Application One cup is 2– 4 gallons. Simplify this expression. = Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Example: Application A sand fly may have a wingspan up to 5– 3 m. Simplify this expression. 5 -3 m Holt Mc. Dougal Algebra 1 =

6 -1 Integer Exponents Example: Application Simplify. A. 4– 3 B. 70 7º = 1 C. (– 5)– 4 D. – 5– 4 Holt Mc. Dougal Algebra 1

6 -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 Mc. Dougal Algebra 1

6 -1 Integer Exponents Simplify. a. 10– 4 b. (– 2)– 4 c. (– 2)– 5 d. – 2– 5 Holt Mc. Dougal Algebra 1 Example: Application

6 -1 Integer Exponents Example : Evaluating Expressions Evaluate the expression for the given value of the variables. x– 2 for x = 4 Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents Example: Application Evaluate p– 3 for p = 4. Holt Mc. Dougal Algebra 1

6 -1 Integer Exponents What if you have an expression with a negative exponent in a denominator, such as ? We know that: So evaluating: Holt Mc. Dougal Algebra 1 or

6 -1 Integer Exponents Example Simplify. A. 7 w– 4 Holt Mc. Dougal Algebra 1 B.

6 -1 Integer Exponents Simplify. a. 2 r 0 m– 3 Example Note: rº = 1 and b. Holt Mc. Dougal Algebra 1 c. .

6 -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 1 5. – 112 Holt Mc. Dougal Algebra 1

6 -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 Mc. Dougal Algebra 1 for a = 6 and b = 3