3-2 Properties of Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

3-2 Properties of Exponents Warm Up Evaluate b 2 for b = 4 4. n 2 r for n = 3 and r =

3-2 Properties of Exponents Learn to apply the properties of exponents.

3-2 Properties of Exponents The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product = 7 4 (7 7 7) 7 = = 7 4 (7 7) (7 7) = = 7 4

3-2 Properties of Exponents

3-2 Properties of Exponents Example 1: Multiplying Powers with the Same Base A B. n 5 n 7 n 12 n Add exponents. Multiply. Write the product as one power.

3-2 Properties of Exponents D C Think: 2 = 2 1 Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

3-2 Properties of Exponents Check It Out E F. x 2 x 3 x 5 x Add exponents. Multiply. Write the product as one power.

3-2 Properties of Exponents H G. x 5 y Check It Out Multiply. Write the product as one power. Cannot combine; the bases are not the same. Add exponents. x 5 y 2

3-2 Properties of Exponents Notice what occurs when you divide powers with the same base. 5  5  55  5  = 5  5  5  5  5 = 5  5 = 5 2 = 5  5  55  5  5 5  5  5  5  5

3-2 Properties of Exponents Subtract exponents – Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

3-2 Properties of Exponents Subtract exponents – Check It Out Divide. Write the product as one power. C. D. e 10 e 5 Subtract exponents. e 10 – 5 e 5

3-2 Properties of Exponents Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 5 4

3-2 Properties of Exponents Simplify. Multiply exponents. Example 3: Raising a Power to a Power A. (5 4 ) 2 (5 4 ) B. (6 7 ) 9 (6 7 ) Multiply exponents.

3-2 Properties of Exponents Simplify. Multiply exponents. Example 3: Raising a Power to a Power C. D. (17 2 ) –20 (17 2 ) – –20 17 –40 Multiply exponents – –3

3-2 Properties of Exponents Simplify. Multiply exponents. Check It Out D. (3 3 ) 4 (3 3 ) E. (4 8 ) 2 (4 8 ) Multiply exponents.

3-2 Properties of Exponents Simplify. Multiply exponents. Check It Out F. G. (13 4 ) –10 (13 4 ) – –10 13 –40 Multiply exponents – –2

3-2 Properties of Exponents Lesson Quiz

3-2 Properties of Exponents Lesson Quiz Write the product or quotient as one power n 7 1. n 3  n t t 9 t 7 6. (m 2 ) 19 m (9 -8 ) 9 9 –72 8. (10 4 ) 0 1