For classroom observation

1. MATHEMATICS 7
SECOND QUARTER

2. 23
base
exponent
= 8
Power of 𝑏𝑥
23
= 2 ∙ 2 ∙ 2

4. THE LAWS OF EXPONENTS
• PRODUCT RULE
• QUOTIENT RULE
• NEAGATIVE EXPONENT RULE
• ZERO EXPONENT RULE
• POWER RULE
• POWER OF THE PROUCT RULE
• POWER OF THE QUOTIENT RULE

5. LEARNING OBJECTIVES
At the end of the lesson, we are expected to:
a. derives the laws of exponents
b. illustrates the laws of exponent; and
c. appreciate the concepts of laws of
exponents as applied in real-life
situation.

6. THE LAWS OF EXPONENTS
a. Product Rule: If 𝑥, 𝑚, and 𝑛 are real numbers, then 𝑥𝑚
∙ 𝑥𝑛
= 𝑥𝑚+𝑛
.
b. Quotient Rule:
b. 1. General rule: If 𝑥, 𝑚, and 𝑛 are real numbers and 𝑥 ≠ 0, then
𝑥𝑚
𝑥𝑛 =
𝑥𝑚−𝑛
, 𝑖𝑓 𝑚 > 𝑛
1
𝑥𝑛−𝑚 , 𝑖𝑓 𝑚 < 𝑛
.
b. 2. Definition of Negative Exponent: If 𝑥 and 𝑚 are real numbers
and 𝑥 ≠ 0, then 𝑥−𝑚
=
1
𝑥𝑚 or
1
𝑥−𝑚 = 𝑥𝑚
.
b. 3. Definition of Zero Exponent: If 𝑚 = 0, then 𝑥𝑚
= 𝑥𝑜
= 1.

7. THE LAWS OF EXPONENTS
c. Power Rule:
c. 1. General Rule: If 𝑥, 𝑚, and 𝑛 are real numbers, then
𝑥𝑚 𝑛
= 𝑥𝑚𝑛
.
c. 2. Power of the Product Rule: If 𝑥, 𝑦, 𝑚, 𝑛 and 𝑝 are real
numbers, then 𝑥𝑚
𝑦𝑛 𝑝
= 𝑥𝑚𝑝
𝑦𝑛𝑝
.
c. 3. Power of the Quotient Rule: If 𝑥, 𝑦, 𝑚, 𝑛 and 𝑝 are real
numbers and 𝑦 = 0, then
𝑥𝑚
𝑦𝑛
𝑝
=
𝑥𝑚𝑝
𝑦𝑛𝑝 .

9. SCIENTIFIC NOTATION
Scientific notation is in the form of
𝑎 × 10𝑛
, where 1 ≤ 𝑎 < 10 and 𝑛 is
an integer.

10. SCIENCE
Photon, also called light quantum, minute energy packet of electromagnetic
radiation. The concept originated (1905) in Albert Einstein’s explanation of the
photoelectric effect, in which he proposed the existence of discrete energy
packets during the transmission of light. Earlier (1900), the German physicist Max
Planck had prepared the way for the concept by explaining that heat radiation is
emitted and absorbed in distinct units, or quanta. The concept came into general
use after the U.S. physicist Arthur H. Compton demonstrated (1923) the
corpuscular nature of X-rays. The term photon (from Greek phōs, phōtos, “light”),
however, was not used until 1926.
A photon travels at approximately 3 × 108 meters per second. If a year is
approximately 3.15 × 107 seconds, how far would be a photon travel in one
year?

11. ECONOMICS
Last July 23, 2020, it was reported by the ABS-CBN News that almost $7.76B or Php386.6B
(3.866 × 1011) is the dept of the Philippines from different international banks to fight
against COVID-19 and interest is not yet being added to it. How can the Philippines pay off
this dept? What is the effect of this dept to the people of the Philippines?
Tax is a compulsory financial charge imposed to taxpayer by a government
organization in order to fund government spending and various public
expenditures.
According to the National QuickStat(NQS), the total population as of 2015 has
an estimation of 100.981 million (1.00981 × 108
) people, reported by the
Philippine Statistics Authority (PSA) as of December 2020. Using this
estimation, calculate the per person share of the national dept. Write your
answer with 4 significant digits.

12. Direction. Simplify the following with positive exponents.
1. 2𝑥 ∙ −3𝑥7
∙ 𝑥4
2.
𝑎5𝑏2
𝑎3𝑏2
3.
𝑥2𝑦3𝑧5
𝑥−3𝑦8𝑧−2
0
4.
𝑥−2𝑦2𝑧2
𝑥−4𝑦3𝑧2
3
5.
6𝑚5𝑛2
4𝑚−2𝑛3
−2

13. ASSIGNMENT
Direction: Solve the given problem. Show the steps in solving the problem.
A company is designing a computer chip that is 5 × 10−9
meters by 7 × 10−9
meters.
Find the area of the computer chip. Write your answer with 4 significant digits.
(𝑛𝑜𝑡𝑒: 𝐴 = 𝑙𝑤)
Variable: Let 𝑙 as the length of the computer chip
𝑤 as the with of the computer chip
𝐴 as the Area of the computer chip
• Given:
• Unknown:
• Solution:
• Final Answer.