This PowerPoint lesson teaches students about exponents and the three laws of exponents: 1) The product law which states that when multiplying like bases, add the exponents. 2) The quotient law which states that when dividing like bases, subtract the exponents. 3) The power law which states that when raising a monomial to a power, multiply the coefficient and exponents. Examples are provided to demonstrate applying each law to simplify exponential expressions. An activity is also included for students to practice identifying and applying the correct law.

2. TOPIC:
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ACTIVITY
AGREEMENT
UNLOCKING
DIFFICULTY
REFERENCES
OBJECTIVES
LESSON
EVALUATION

3. OBJECTIVES
1. defines
exponential
expressions
2. applies the laws of
exponents in
simplifying
exponential
expressions

4. UNLOCKING DIFFICULTIES
73
Exponent
Base Power

5. LESSON
In an expression of the form xn , x is the base and n is the
exponent, and the quantity xn is called power. The exponents
indicates the number of times that the base is used as s factor.
xn = x . x . x. . . x . x . x
Base Exponent
x is a factor n times
xn is read
as ‘x to the
nth power’

6. Law 1 – Product Rule
am ● an = am + n (when multiplying like bases add the
exponent)
Examples:
1. 52 ● 56 = 5 2+6 = 58
2. a5 ● a2 ● a7 = a5 + 2 + 7 = a14
3. (2x4)(3x3) = (2●3)(x4+3) = 6x7
4. (-3x4y2)(4x5y3) = (-3●4)(x4+5)(y2+3) = -12x9y5

7. Law 2 – Quotient Law
am ÷ an = am - n (when dividing like bases subract the
exponent. Note:it is always the numerator’s power
minus the denominator’s power )
Examples:
1. 59 ÷ 56 = 5 9-6 = 53
2. a5 ÷ a2 ● a7 = a5 + 2 + 7 = a14
3 (12𝑥9) ÷ (3𝑥3) = (12÷3)(x9-3) = 4x6
4. .
−21𝑥7 𝑦8
7𝑥5 𝑦3 = (-21÷7)(x7-5)(y8-3) = -3x2y5
In expanded form:
𝑥5
𝑥2 =
𝑥.𝑥.𝑥.𝑥.𝑥
𝑥.𝑥.
= x2

8. Law 3. Power Law
(ambm)n = amnbmn (when taking a monomial to a
power multiply the powers including the coefficient)
Examples:
1. (a2)3 = a6
2. (-m3)4 = m12 , (-m3)3 = -m9
3. (x3y4)2 = x6y8
4. (3r3s7t4)3 = 33r9s21t12 = 27r9s21t12
5. (-2x5y7z6)5 = (-2)5x25y35z30 = -32x25y35z30

9. ACTIVITY
Determine what law are you going to
apply to simplify the expression
1. (x3)2
2. (3x6)(-4x9)
3.
𝑟11
𝑟8
4. (4x2y4z6)6
Power Law
Product Law
Quotient Law
Power Law

10. EVALUATION
Simplify.
1. 2m3 ● 2m4
2. 2k4 ● 4k7
3. (y5)3
4.
9𝑚8
3𝑚5
5. (-6x7y2z6)3

11. AGREEMENT
Simplify. Should contain only positive exponent.
1.
𝑥7
𝑥4
2.
𝑥2
𝑥5
3.
𝑥8
𝑥8

12. REFERENCES
Learning Module in Mathematics 9
Kutasoftware