1. Evaluating Algebraic Expressions 4-3 Properties of Exponents California Standards NS2.3 Understand negative whole- number exponents. Multiply and divide expressions involving exponents with a common base. NS2.1 Multiply, divide, and simplify rational numbers by using exponent rules.

2. Evaluating Algebraic Expressions 4-3 Properties of Exponents The following suggests a rule for multiplying powers with the same base. 2 4 2 2 = (2 2 2 2) (2 2) = 2 6 a 3 a 2 = (a a a) (a a) = a 5 Notice that the sum of the exponents in each expression equals the exponent in the answer: 4 + 2 = 6 and 3 + 2 = 5.

3. Evaluating Algebraic Expressions 4-3 Properties of Exponents

4. Evaluating Algebraic Expressions 4-3 Properties of Exponents Additional Example 1: Multiplying Powers with the Same Base A. 6 6 6 3 6 9 6 6 + 3 B. n 5 n 7 n 12 n 5 + 7 Add exponents. Simplify each expression. Write your answer in exponential form.

5. Evaluating Algebraic Expressions 4-3 Properties of Exponents Check It Out! Example 1 A. 4 2 4 4 4 6 4 2 + 4 B. x 2 x 3 x 5 x 2 + 3 Add exponents. Simplify each expression. Write your answer in exponential form.

6. Evaluating Algebraic Expressions 4-3 Properties of Exponents RAISING A POWER TO A POWER Reading Math (9 4 ) 5 is read as “nine to the fourth power, to the fifth power.”

7. Evaluating Algebraic Expressions 4-3 Properties of Exponents Simplify each expression. Write your answer in exponential form. Multiply exponents. Additional Example 3: Raising a Power to a Power A. (5 4 ) 2 (5 4 ) 2 5 4 2 5858 B. (6 7 ) 9 (6 7 ) 9 6 7 9 6 63 Multiply exponents.

8. Evaluating Algebraic Expressions 4-3 Properties of Exponents Multiply exponents. Additional Example 3: Raising a Power to a Power C. D. (17 2 ) –20 17 2 –20 17 –40 2323 12 –3 Simplify each expression. Write your answer in exponential form. 2323 –36

9. Evaluating Algebraic Expressions 4-3 Properties of Exponents Multiply exponents. Check It Out! Example 3 A. (3 3 ) 4 (3 3 ) 4 3 3 4 3 12 B. (4 8 ) 2 (4 8 ) 2 4 8 2 4 16 Multiply exponents. Simplify each expression. Write your answer in exponential form.

10. Evaluating Algebraic Expressions 4-3 Properties of Exponents Multiply exponents. Check It Out! Example 3 C. D. (13 4 ) –10 13 4 –10 13 –40 1414 11–2 Simplify each expression. Write your answer in exponential form. 1414 –22