Math

1. APPLIES THE LAWS INVOLVING
POSITIVE INTEGRAL EXPONENTS
TO ZERO AND NEGATIVE INTEGRAL
EXPONENTS
(M9AL-IID-1)

2. What are the different
variations? How will you relate it
to real life applications?

3. Activity 1: Remember me this way! Simplify the
expressions.
1. 𝑏5(𝑏3) =
2. (−2)3
=
3. (−2)3(−2)3=

4. Objectives:
•Review laws of Exponents.
•Applies the quotient rule to fraction
where the exponent in the
numerator and the denominator
are the same.

5. Exponent Rule
•Exponent rules are those laws that are used for
simplifying expressions with exponents. Many
arithmetic operations like addition, subtraction,
multiplication, and division can be conveniently
performed in quick steps using the laws of exponents.
These rules also help in simplifying numbers with
complex powers involving fractions, decimals, and
roots.

6. Exponent
82
Exponent/index/
power
base

7. LAWS OF EXPONENT
•Product of Power
•Quotient of a Power
•Power of Power Rule
•Power of Product
•Power of Quotient

8. Product Rule
The product rule of exponents is used to multiply expressions
with the same bases. This rule says, "To multiply two expressions
with the same base, add the exponents while keeping the base
the same." This rule involves adding exponents with the same
base. Here the rule is useful to simplify two expressions with a
multiplication operation between them.
𝑎𝑚
(𝑎𝑛
) = 𝑎𝑚+𝑛
Example:
52
(53
) = 52+3
= 55
= (5)(5)(5)(5)(5) = 3,125

9. Power of Product Rule
The 'power of a product rule of exponents' is used to find the result of a product that
is raised to an exponent. This law says, "Distribute the exponent to each
multiplicand of the product."
(𝒂𝒃)𝒎
= 𝒂𝒎
𝒃𝒎
Example:
(𝑥𝑦)2
= 𝑥2
𝑦2

10. Quotient Rule
The quotient law of exponents is used to divide expressions with the same bases. This
rule says, "To divide two expressions with the same base, subtract the exponents while
keeping the base same." This is helpful in solving an expression, without actually
performing the division process. The only condition that is required is that the two
expressions should have the same base
𝑎𝑚 ÷ 𝑎𝑛 = 𝑎𝑚−𝑛
25
23
= 25−3
= 22
= 2(2) = 4

11. Power of Quotient
The power of a quotient rule of exponents is used to find the result of a
quotient that is raised to an exponent. This law says, "Distribute the
exponent to both the numerator and the denominator." Here, the bases
are different and the exponents are the same for both the bases.
𝑎
𝑏
𝑚
=
𝑎𝑚
𝑏𝑚
• Example:
𝑎
𝑏
5
=
𝑎5
𝑏5

12. Power of Power Rule
The 'power of a power law of exponents' is used to simplify
expressions of the form (am)n. This rule says, "When we
have a single base with two exponents, just multiply the
exponents." The two exponents are available one over the
other. These can be conveniently multiplied to make a
single exponent.
(𝑎𝑚
)𝑛
= 𝑎𝑚𝑛
Example:
(22
)3
= 26
= 2 2 2 2 2 2 = 32

13. Directions: Answer the following
questions orally.
•1. What will you do with the exponents when
you are:
• Multiplying powers?
• Dividing powers?
• Raising a power to power?
• Raising a product of power to power?
• Raising a fraction to a power?

14. What are the different
laws of exponents?

15. Assignment
1.) 52
. 53
=
2.) 𝑥2𝑦2. 𝑥6𝑦7 =
3.) 2.2. 23
=
4. 6abc 5𝑎3
𝑐2
=
5. 64
÷ 62
=