1. Properties of Exponents – Part 1 Learn multiplication properties of exponents.

2. 43210 In addition to 3, student will be able to go above and beyond by applying what they know about working with integer exponents. The student will be able to work with integer exponents. - Know and apply the properties of exponents. - Simplify numerical expressions with exponents. - Perform operations with scientific notation. With no help the student has a partial understanding of integer exponents. - Is able to use scientific notation to estimate very large or very small numbers. - Interpret scientific notation generated by technology. With help, the student may have a partial understanding of how to work with integer exponents. Even with help, the student is unable to work with integer exponents. Focus 11 - Learning Goal: The student will be able to work with integer exponents.

3. 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 7 7 7 = 7 4 (7 7 7) 7 = 7 3 7 1 = 7 4 (7 7) (7 7) = 7 2 7 2 = 7 4

4. Words NumbersAlgebra To multiply powers with the same base, keep the base and add the exponents. b m b n = b m + n 3 5 3 8 = 3 5 + 8 = 3 13 MULTIPLYING POWERS WITH THE SAME BASE

5. Multiplying Powers with the Same Base 1. 6 6 6 3 6 9 6 6 + 3 2. n 5 n 7 n 12 n 5 + 7 Add exponents. Multiply. Write the product as one power.

6. 4. 24 4 24 4 3. 2 5 2 2 6 2 5 + 1 24 8 4 + 4 Think: 2 = 2 1 Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

7. Power of Power Property (2 4 ) 6 = 2 24 Powers of powers with the same base: (a m ) n = a mn multiply exponents 2 (46)

8. Power of a Product Property Different bases, distribute power to each base and multiply. Examples: (a b) 4 = a 4 b 4 = a 4 b 4 (-3x) 2 = (-3) 2 x 2 = 9x 2

9. Practice! 1. (3 2 y 3 ) 2 1. 3 (22) y (32) 2. 3 4 y 6 3. 81y 6 2. (5a 2 b 4 ) 5 1. 5 5 a (25) b (45) 2. 5 5 a 10 b 20

10. Practice! 1. n 3  n 4 2. 3 3 3 2 3 5 3. (-4xy 3 ) 3 4. 8 8 8 1. n 7 2. 3 10 3. -64x 3 y 9 4. 8 9