Negative Exponents Chapter 4 Section 4.6

Objective Students will solve problems involving negative exponents

Concept You have learned the meaning of an when n is a positive number. For example: 23 = 8 22 = 4 21 = 2

Concept In this lesson you will consider the meaning of expressions like 20 and 2-1 that have zero and negative integers as exponents.

Definition of a-n If a is a nonzero real number and n is a positive integer, a-n = 1/an

Example 10-3 5-4 16-1

concept m > n am/an = am-n = a7/a3 = a7-3 = a4 m < n am/an = 1/an-m = a3/a7 = 1/a7-3 = 1/a4 m = n am/an = am-n = a0 = a5/a5 = a5-5 = a0 = 1

If a is a nonzero real number a0 = 1 The expression 00 has no meaning Definition of a0 If a is a nonzero real number a0 = 1 The expression 00 has no meaning

Concept a5 = a5-5 = a0 a5 But you already know that a5 = 1 This is what leads us to the previous definition (a0)

concept Multiplying like bases, add exponents Dividing like bases, subtract exponents Numbers raised to exponents, goes to all numbers Power to a Power, multiply exponents

Example Simplify. Give your answers using positive exponents 5/5-3 (b-1)-3 (3x-1)2

Questions

Assignment Worksheet