1. Holt Algebra 1 7-1 Integer Exponents Warm Up(Add to Notes) Evaluate each expression for the given values of the variables. 1. x 3 y 2 for x = –1 and y = 10 2. for x = 4 and y = (–7) –100

2. Holt Algebra 1 7-1 Integer Exponents 7-1 Integer Exponents Holt Algebra 1

3. 7-1 Integer Exponents Base x Exponent Remember! 4

4. Holt Algebra 1 7-1 Integer Exponents

5. Holt Algebra 1 7-1 Integer Exponents Notice the phrase “nonzero number” in the previous table. This is because 0 0 and 0 raised to a negative power are both undefined.

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

7. Holt Algebra 1 7-1 Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4 –3 B. 7 0 7º = 1 Any nonzero number raised to the zero power is 1. C. (–5) –4 D. –5 –4

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

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

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

11. Holt Algebra 1 7-1 Integer Exponents Check It Out! Example 3b Evaluate the expression for the given values of the variables. for a = –2 and b = 6 2 Substitute –2 for a and 6 for b. Evaluate expressions with exponents. Write the power in the denominator as a product. Evaluate the powers in the product. Simplify.

12. Holt Algebra 1 7-1 Integer Exponents 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.

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

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

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

16. Holt Algebra 1 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. 6 0 5. –11 2 1 –121

17. Holt Algebra 1 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. for a = 6 and b = 3

18. Holt Algebra 1 7-1 Integer Exponents Warm-Up 1. A square foot is 3 –2 square yards. Simplify this expression. Simplify. 2. 2 –6 3. (–7) –3 4. 6 0 5. –11 2 1 –121