6 1 Zero Negative Exponents Objective IWBAT simplify
6 -1 Zero & Negative Exponents Objective: IWBAT simplify and evaluation expressions with a zero exponent and a negative exponent.
Warm up Simplify 32 = 3*3 1 23 = = 9 1 = 1 2*2*2 8
Bell Work Blitz Complete the Bell Work Blitz : Create a system of linear inequalities that has no solution. Demonstrate by creating a graph. 5 minutes 10 points
6 -1 Integer Exponents 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. 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 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 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 1: Application One cup is 2– 4 gallons. Simplify this expression. gal is equal to Holt Mc. Dougal Algebra 1
6 -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 Mc. Dougal Algebra 1
Brain Break • What kind of people use negative exponents? • Economists, Biologists, Geologists, Chemists, Engineers, Computer Programmers, … • Can you think of any others? • Where would we see negative exponents in our world outside of school? • Did you know that negative exponents means exponential decay? Why do you think that is? • Yes, decay could mean gets smaller and smaller. Then exponential decay means your number is becoming smaller and smaller via a negative exponent!!
6 -1 Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4– 3 B. 70 7º = 1 C. (– 5)– 4 D. – 5– 4 Holt Mc. Dougal Algebra 1 Any nonzero number raised to the zero power is 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 Check It Out! Example 2 b. (– 2)– 4 c. (– 2)– 5 d. – 2– 5 Holt Mc. Dougal Algebra 1
6 -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 Mc. Dougal Algebra 1
6 -1 Integer Exponents Example 3 B: Evaluating Expressions with Zero and Negative Exponents Simplify 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. Simplify the denominator. Simplify. Holt Mc. Dougal Algebra 1
6 -1 Integer Exponents Wrap Up 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 1 – 121 Holt Mc. Dougal Algebra 1
Ticket Out the Door • Quick write: How would you use negative exponents in the real world? Where would you look for evidence to support your answer?
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