Grade 7 Math LESSON 21: LAWS OF EXPONENTS
LEARNING GUIDE
GRADE 7 MATH LEARNING GUIDE
Lesson 21: Laws of Exponents
Time: 1.5 hours
Pre-requisite Concepts: Multiplication of real numbers
About the Lesson: This lesson is all about the laws of exponents.
Objectives:
In this lesson, the students must be able to:
1) define and interpret the meaning of an where n is a positive integer;
2) derive inductively the Laws of Exponents (restricted to positive integers)
3) illustrate the Laws of Exponents.
Lesson Proper
I. Activity 1
Give the product of each of the following as fast as you can.
1) 3 x 3 = ________
2) 4 x 4 x 4 = ________
3) 5 x 5 x 5 = ________
4) 2 x 2 x 2 = ________
5) 2 x 2 x 2 x 2 = ________
6) 2 x 2 x 2 x 2 x 2 = ________
II. Development of the Lesson
Discovering the Laws of Exponents
A) an = a x a x a x a ….. (n times)
In an, a is called the base and n is called the exponent
Exercises
1) Which of the following is/are correct?
a) 42 = 4 x 4 = 16
b) 24 = 2 x 2 x 2 x 2 = 8
c) 25 = 2 x 5 = 10
d) 33 = 3 x 3 x 3 = 27
2) Give the value of each of the following as fast as you can.
a) 23
b) 25
c) 34
d) 106
Activity 2
Evaluate the following. Investigate the result. Make a simple conjecture on it. The first two are
done for you.
1) (23)2 = 23 • 23 = 2 • 2 • 2 • 2 • 2 • 2 = 64
2) (x4)3 = x4 • x4 • x4 = x • x • x • x • x • x • x • x • x • x • x • x = x12
3) (32)2 =
4) (22)3 =
5) (a2)5=
AUTHOR: Lambert G. Quesada
1 Grade 7 Math LESSON 21: LAWS OF EXPONENTS
LEARNING GUIDE
Did you notice something?
What can you conclude about (an)m? What will you do with a, n and m?
What about these?
1) (x100)3
2) (y12)5
Activity 3
Evaluate the following. Notice that the bases are the same. The first example is done for you.
1) (23)(22) = 2 • 2 • 2 • 2 • 2 = 25 = 32
2) (x5)(x4) =
3) (32)(34) =
4) (24)(25) =
5) (x3)(x4) =
Did you notice something?
What can you conclude about an • am? What will you do with a, n and m?
What about these?
1) (x32)(x25)
2) (y59)(y51)
Activity 4
Evaluate each of the following. Notice that the bases are the same. The first example is done for
you.
1)
=
2)
=
3)
=
4)
=
= 16
--- remember that 16 is the same as 24
Did you notice something?
What can you conclude about
? What will you do with a, n and m?
What about these?
1)
2)
AUTHOR: Lambert G. Quesada
2 Grade 7 Math LESSON 21: LAWS OF EXPONENTS
LEARNING GUIDE
Summary:
Laws of exponent
1) an = a • a • a • a • a….. (n times)
2) (an)m = anm
power of powers
3) an • am = am+n
product of a power
4)
=an – m
5) a0 = 1
quotient of a power
where a ≠ 0
law for zero exponent
What about these?
a) (7,654,321)0
b) 30 + x0 + (3y)0
Exercise:
Choose a Law of Exponent to apply. Complete the table and observe. Make a conjecture.
No.
Result
Applying a law GIVEN (Start
ANSWER
REASON
of Exponent
here)
1)
2)
3)
4)
6) a-n and
law for negative exponent
Can you rewrite the fractions below using exponents and simplify them?
a)
b)
c)
What did you notice?
AUTHOR: Lambert G. Quesada
3 Grade 7 Math LESSON 21: LAWS OF EXPONENTS
LEARNING GUIDE
What about these?
d) x-2
e) 3-3
f) (5-3)-2
III. Exercises
A. Evaluate each of the following.
1)
2)
3)
4)
5)
28
82
5-1
3-2
180
(23)3
(24)(23)
(32)(23)
x0 + 3-1 – 22
[22 – 33 + 44]0
6)
7)
8)
9)
10
B. Simplify each of the following.
1) (x10)(x12)
7)
2) (y-3)(y8)
8)
3) (m15)3
9)
4) (d-3)2
10)
5) (a-4)-4
11)
6)
Summary
In these lessons, you learned some laws of exponents.
AUTHOR: Lambert G. Quesada
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