8 1 Multiplication Properties of Exponents Focus 8

8. 1 Multiplication Properties of Exponents

Focus 8 Learning Goal – (HS. N-RN. A. 1 & 2, HS. A-SSE. B. 3, HS. A-CED. A. 2, HS. F-IF. B. 4, HS. FIF. C. 8 & 9, and HS. F-LE. A. 1) = Students will construct, compare and interpret linear and exponential function models and solve problems in context with each model. 4 3 2 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model. - Compare properties of 2 functions in different ways (algebraically, graphically, numerically in tables, verbal descriptions) - Describe whether a contextual situation has a linear pattern of change or an exponential pattern of change. Write an equation to model it. - Prove that linear functions change at the same rate over time. - Prove that exponential functions change by equal factors over time. - Describe growth or decay situations. - Use properties of exponents to simplify expressions. Students will construct, compare, and interpret linear function models and solve problems in context with the model. - Describe a situation where one quantity changes at a constant rate per unit interval as compared to another. 1 0 Students will have Even with help, partial success at the student is not a 2 or 3, with help. successful at the learning goal.

Exponent Vocabulary an = a • a…. . an times Base number: the number being multiplied. a is the base number. Power: the number of times the base is multiplied. n is the power.

Rules for multiplying with exponents when you have the SAME BASE! PRODUCT OF POWERS PROPERTY Multiplication with the same base: m a • n a = m+n a add exponents

POWER OF POWER PROPERTY Powers of powers with the same base: m n (a ) = mn a multiply exponents

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 (-3 x)2 = (-3) 2 • x 2 = 9 x 2

Try these! 1. 69 = 5 4 66 10, 077, 696 3. (2 x)3 23 x 3 = 2. 2 9 10 10 1011 = 100, 000, 000 4. [(5 x)3]6 8 x 3 (5 x)18 = 5 18 x 18

Something fun to do with exponents… a>1 the equation is a model for exponential growth. a<1 the equation is a model for exponential decay.

Example: ax Graph Growth 2 x Decay 0. 6 x

Some final exponent practice problems… 3 y 2 (2 y)3 3 y 2 23 y 3 =3 23 y 5 =24 y 5 (r 2 st 3)2(s 4 t)3 = r 4 s 2 t 6 s 12 t 3 = r 4 s 14 t 9