Grace is saving money each day according to an exponential pattern. On day 1 she saves ₱3, day 2 she saves ₱9 (3 x 3), day 3 she saves ₱27 (3 x 3 x 3), and day 4 she saves ₱81 (3 x 3 x 3 x 3). The problem asks how much Grace will save on day 7 and the total amount saved over 7 days. To solve this, we recognize the pattern of multiplying the previous amount by 3 each day and write the terms using exponential notation. This allows us to determine Grace will save ₱2187 (3 x 3 x 3 x 3 x 3 x 3 x 3 x ₱3

1. LESSON 4:
Exponential Notation

2.  LessonOutcomes
At the end of the lesson, you should be able to:
• Describe the exponent and the base in a number
expresses in exponential notation.
• Give the value of numbers expressed in exponential
notation.
• Perform two or more different operations on whole
numbers with or without exponents and grouping
symbols and;
• Solve word problems involving exponential notation.

3. There are 28 cartons of milk in a grocery store. How many cartons of
milk are there?
What does 28 mean?
• 28 is an example of a number written in exponential notation.
• It is read as “2 to the eighth power”, “two to the eighth” or “2 raised to
8”.
Base 28 Exponent
• 2 is the base. It is a number that gets multiplied repeatedly a certain
number of times. It is written in regular size.
• 8 is the exponent.The exponent tells the number of times the base is
to be multiplied by itself. It is written smaller in the upper right of the
base.

4. When written in expanded form, 28 is equal to 2 x 2 x 2 x 2 x 2 x
2 x 2 x 2.The standard form of 28 is 256.
Therefore, there are 256 cartons of milk in a grocery store.
Base Exponent Exponential
notation
Read As Standard
Form
12 x 12 12 2 122 Twelve squared 144
4 x 4 x 4 4 3 43 Four cubed 64
10 x 10 x 10 10 3 103 Ten cubed 1000
5 2 52 Five squared 25
5 x 5
Factor or expanded
form

5. Each side of a square is 4 centimeters long. Find the area of the square.
4 cm
To find the area of the square:
Area of the square = side x side
= 4cm x 4 cm
=16 cm2
We can write 4 x 4 as 42
4 is called the base.
2 is called the exponent.
42 is the example of a number written in exponential notation.
42 is read as “4 to the second power”, “4 raised to the power of 2”,
“the square of 4” or “4 squared”.

6. A cubed has edges of 6 centimeters long. What is the volume?
6cm
6cm
6cm
To find the volume of a cube
Volume of the cube = 6 cm x 6 cm x 6 cm
= 216 cm3
6 x 6 x 6 is called the cube of 6.
We can write 6 x 6 x 6 as 63
6 is the Base, 3 is the exponent.
63 is read as:
The cubed of 6, 6 to the third power, 6 raised
to the power of 3.

7. Let’s practice
Exponential Notation Base Exponent Factored Form
1. 34
2. 82
3. 133
Factored Form Exponential
Form
Base Exponent
1. 12x12x12x12x12x12
2. 8x8x8x8x8x8x8
3. 2x2x2x2x2x2x2x2
3 4 3 x 3 x 3 x 3
8 2 8 x 8
13 3 13 x 13 x 13
126 12 6
87 8 7
28 2 8

8. Grace saved ₱3.00 on Day 1, ₱9.00 on Day 2, ₱27.00 on Day 3, ₱81.00 on Day 4, and so on. If the
pattern continues, how much will she save on the 7th day? How much will be her total savings?
Let’s analyze
Day Savings
1 ₱3.00
2 ₱9.00
3 ₱27.00
4 ₱81.00
5
6
7
x3
x3
x3
Table 1
Day Repeated Multiplication Exponential Notation Savings
1 ₱3.00 31 ₱3.00
2 3 x ₱3.00 32 ₱9.00
3 3 x 3 x₱3.00 33 ₱27.00
4 3 x 3 x 3 x ₱3.00 34 ₱81.00
5 3 x 3 x 3 x 3 x ₱3.00
6 3 x 3 x 3 x 3 x 3 x ₱3.00
7 3 x 3 x 3 x 3 x 3 x 3 x₱3.00
TOTAL
Table 2
₱243.00
₱729.00
₱2187.00
35
36
37
₱3729.00
Answer: Grace will save ₱2187.00 on Day 7
Her total savings in seven days will be ₱3729.00

9. Examples
1.) 92
2.) 45
92 means 9 is used as a factor 2 times.
92 is 9 x 9 in expanded form
The value of 92 is 81
45 means 4 is used as a factor 5 times.
45 is 4 x 4 x 4 x 4x 4 in expanded form
The value of 45 is 1024
Review
• A number expressed in exponential notation is composed of a base and a
exponent.
• It is a “shorthand” way of writing repeated multiplication.
• The base is the number used as a repeated factor and the exponent indicates
the number of times you are going to multiply the base or is used as factor.
• The exponent is placed at the upper right side of the base.

10. Activity in Lesson 4
Complete the table using the given description or situation.Write your answers on
your answer sheet.
Description Base Exponent Exponential
Notation
1)The number 7 is raised to the power of 11 7 11 711
2) 34 is used as a factor eight times
3) Letter x is the base. It is used as factor 20 times.
4) Mara holds a piece of paper with “74 cubed” written on it.
5) Steve's answer to the problem is 19. he wants to raise it to the sixth
power.
6)Letter n represents the number of times 25 is used as a factor.
7)The whole number is 59. on its upper right side a smaller number 4 is
written.
8)The teacher instructed his pupils to write the exponential notation
which means 45 is used as a factor 7 times.
9)You are dinos friend. Help him identify the base and exponent in the
exponential notation 866.
10)Number 8 represents the number of times letter n is used as a factor.