Republic of the Philippines

Department of Education

Regional Office IX, Zamboanga Peninsula

9 Z est for P rogress

Z eal of P artnership

Quarter 2 – Module 3:

Zero and Negative Exponents

Name of Learner:

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Grade & Section:

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Name of School:

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Math Module – Grade 9

Alternative Delivery Mode

Quarter 2 – Module 3: Zero and Negative Exponents

First Edition, 2020

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Undersecretary: Diosdado M. San Antonio

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Department of Education: Region IX, Schools Division of Zamboanga del Norte

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Development Team of the Module Writer: Armil O. Turtor

Reviewer: ISMAEL K. YUSOPH

Management Team: SDS: Ma. Liza R. Tabilon, Ed.D, CESO V ASDS: Dr. Ma. Judelyn J. Ramos

ASDS: Dr. Armando P. Gumapon ASDS: Dr. Judith V. Romaguera

CID CHIEF: Lilia E. Abello, Ed.D EPS-LRMS: Evelyn C. Labad

EPS-MATH: Ismael K. Yusoph

PSDS: Antonina D. Gallo, Ed.D.

Principal: Daisy Flor J. Romaguera

What I Need to Know

This module covers key concepts of integral exponents .You will learn

more about applying the laws of positive integral exponents to zero and negative

integral exponents.

Lesson 1

• Zero and Negative Exponents

In this lesson you will learn to:

• apply the laws involving positive integral exponents to zero and

negative integral exponents; (M9AL- IId-1)

• simplify exponential expressions using the laws of integral exponent.

(M9AL- IId-1)

Lesson

1

Zero and Negative

Exponents

What’s In

Simplify the following expressions:

1. x3y2 xy

2. (2a3)4

3. c3x • c2 +4x

3

4. 4x2 y3

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Questions:

1. How did you simplify the given expressions?

2. What concepts have you applied?

3. What laws of integral exponents did you use in simplifying the

expressions?

What’s New

Analyze the problem below then answer the questions that follow.

A grain of rice has a volume of 20-9 m3. A box full of rice has a

volume of 20-3 m3.How many grains of rice are there in the

box?

Questions:

1. What have you noticed from the values given in the problem?

2. What have you observed from the exponents?

3. What have you done to simplify these values?

4. How did you solve the problem?

5. Have you applied any law? What are the laws you applied to answer the

problem?

Questions:

1. What did you observe about the exponents?

2. How were the problems solved?

3. What can you say about the process of solving problems?

What is It

The laws of exponents can also be extended to include zero and

negative integers.

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A. Zero and Negative Exponents

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D. Rewriting Algebraic Expressions with Zero and Negative Exponents

When algebraic expressions have zero and negative exponents, they have to

be rewritten in a way that all exponents must be positive. In all cases, it is

assumed that all denominators are not equal to zero.

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The laws of exponents for division can be summarized, such that;

E. Simplifying Exponential Expressions

Exponential expressions are said to be in simplest form if:

1. all the exponents are positive;

2. there are no powers of powers;

3. each base appears only once, and

4. all fractions are in simplest form.

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What’s More

Activity 1. Simplify each expression:

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Questions:

1. Did you get the treasures? How does it feel?

2. How did you simplify the given expressions?

3. What are the concepts/ processes to use in simplifying expressions with

zero and negative integral exponents?

Question:

Who do you think is correct in simplifying the given expression? Justify your

answer.

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Activity 4.

Analyze and solve the problem below.

Questions:

1. How many grams can it reach during its life cycle?

2. How did you apply your understanding of exponents in solving the

problem?

3. What necessary concepts/ skills needed to solve the problems?

4. What examples can you give that show the application of zero and

negative integral exponents?

5. Are exponents important in solving real-life problems? Why?

3. Exponential expressions are in simplest form if:

a. all the exponents are positive;

b. there are no powers of powers;

c. each base appears only once; and

d. all fractions are in simplest form.

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What I Have Learned

What I Can Do

A. Solve the problem.

1. The diameter of a red blood cell is about 7.5 x 10-4 cm, and the diameter of

a white blood cell is about .0015 cm. Which blood cell is larger and by how

many times?

B. List some real-life situations which involve exponents.

Assessment

Simplify the following expressions with zero and negative exponents.

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Answer Key

REFERENCES

Jose-Dilao, Soledad and Bernabe , Julieta G, Intermediate Algebra ,Revised

Edition

Mathematics 9 Learner’s Module Next

Generation Math

http://www.mathisfun.com

{ HYPERLINK "http://www.mathbitsnotebook.com" } {

HYPERLINK "http://www.courses.lumenlearning.com" }

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