LESSON 1-3 EXPONENTS

Learn to represent numbers by using exponents.

Vocabulary exponent base exponential form

An exponent tells how many times a number called the base is used as a factor. A number is in exponential form when it is written with a base and an exponent. Exponent 73 Base = 7  7  7= 343

Additional Example 1: Writing Numbers in Exponential Form Write each expression in exponential form. A. 5  5  5  5 B. 3  3  3  3  3 54 5 is a factor 4 times. 35 3 is a factor 5 times.

Additional Example 2: Finding the Value of Numbers in Exponential Form Find each value. A. 26 B. 45 26 = 2  2  2  2  2  2 = 64 45 = 4  4  4  4  4 = 1,024

Understand the Problem Additional Example 3: Problem Solving Application A phone tree is used to contact families at Paul’s school. The secretary calls 4 families. Then each family calls 4 other families, and so on. How many families will be notified during the fourth round of calls? 1 Understand the Problem The answer will be the number of families called in the 4th round. List the important information: The secretary calls 4 families. Each family calls 4 families.

2 Make a Plan You can draw a diagram to see how many calls are in each round. Secretary 1st round – 4 calls 2nd round–16 calls

Solve 3 Notice that in each round, the number of calls is a power of 4. 1st round: 4 calls = 4 = 41 2nd round: 16 calls = 4  4 = 42 So during the 4th round, there will be 44 calls. 44 = 4  4  4  4 = 256 During the 4th round of calls, 256 families will have been notified. Look Back 4 Drawing a diagram helps you see how to use exponents to solve the problem.

Lesson Quiz Write each expression in exponential form. 1. 12  12  12 2. 9  9  9  9  9  9  9 Find each value. 3. 202 4. 64 5. In a phone tree, each of three people will call three people, and then each of those will call three more. If there are five levels of the tree, how many people will be called?