# Exploring Positive and Negative Integer Exponents: Grade 8 Math Lesson

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You are a research biologist studying the life of microorganisms in pond water. In your research study, you observed the number of a certain microorganism doubled each day. You will use integer exponents to record the number of microorganisms each day.

Lesson Objective: Lesson is aligned to the Common Core State Standards for Mathematics – 8.EE.1 Expressions and Equations – Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Materials Required: scientific calculator

## Lesson Procedure

Definition: In the number 43, the base number is 4 and the positive integer exponent is 3. The exponent indicates repeated multiplication of the base number. The number 43 means that the base number, 4, will be multiplied by itself 3 times. There are 3 factors of 4 in the number 43. The base number written with a positive integer exponent, 43 is equal to the repeated multiplication sentence 4 x 4 x 4. So 43 = 4 x 4 x 4

1. Look at the number 54.

• What is the base number?
• What is the integer exponent? Is it positive or negative?
• How many factors of 5 are there?
• Write the repeated multiplication sentence for 54.

2. Look at the repeated multiplication 6 x 6.

• Write a base number and an integer exponent for the repeated multiplication.
• Should you use a positive integer exponent or a negative integer exponent?

1. Look at the number 54.

• What is the base number? 5
• What is the integer exponent? 4. Is it positive or negative? positive
• How many factors of 5 are there? 4
• Write the repeated multiplication sentence for 54. 5 x 5 x 5 x 5 = 54

2. Look at the repeated multiplication 6 x 6.

• Write a base number and an integer exponent for the repeated multiplication. 62
• Should you use a positive integer exponent or a negative integer exponent? positive

Definition: In the number 2-5, the base number is 2 and the negative integer exponent is -5. A number with a negative exponent is the same as the inverse of the number with a positive exponent. The number 2-5, means that the inverse of the base number, 2, will be multiplied by itself 5 times. There are 5 factors of the inverse of 2 in the number 2-5. The inverse of 2 is 1/2. The base number written with a negative exponent, 2-5 is equal to the inverse written with a positive exponent, 1/25, and equal to the repeated multiplication sentence 1/2 x 1/2 x 1/2 x 1/2 x 1/2. So, 2-5 = 1/25 = 1/2 x 1/2 x 1/2 x 1/2 x 1/2.

3. Look at the number 4-3.

• What is the base number?
• What is the integer exponent? Is it positive or negative?
• How many factors of 4 are there?
• What is the inverse of 4?
• Write the repeated multiplication sentence for 4-3.

4. Look at the repeated multiplication 1/6 x 1/6 x 1/6 x 1/6

• Write a base number and an exponent with a negative integer for the repeated multiplication.
• Should you use a positive integer exponent or a negative integer exponent?

3. Look at the number 4-3.

• What is the base number? 4
• What is the integer exponent? -3 Is it positive or negative? Negative
• How many factors of 4 are there? 3
• What is the inverse of 4? 1/4
• Write the repeated multiplication sentence for 4-3. 1/4 x 1/4 x 1/4 = 4-3

4. Look at the repeated multiplication 1/6 x 1/6 x 1/6 x 1/6.

• Write a base number and an exponent with a negative integer for the repeated multiplication. 6-4
• Should you use a positive integer exponent or a negative integer exponent? Negative