Name: _______________________________ Grade & Section: ____________________
Learning Competency : Applies the laws involving positive integral exponents to zero and
negative integral exponents, and rational exponents. (M9AL-lld-1)
Activity Title
: Multiply Me!
Learning Target
: Problem solving using Product Rule
Concept Note
: Demonstrate understanding involving positive integral exponents
to zero and negative integral exponents, and rational exponents.
LAWS OF EXPONENTS: PRODUCT RULE
The product rule for exponents states: xa ⋅ xb= x a+b. We're going to focus on the rule
when a and b are natural numbers. To see why, let's look at the example x2⋅x3. If we expand
these we see
x2⋅x3=(x⋅x)⋅(x⋅x⋅x)
The first term has two factors of x and the second term has three factors of x. When we multiply
these two we see there are now five factors of x.
x2⋅x3=(x⋅x)⋅(x⋅x⋅x)=x⋅x⋅x⋅x⋅x=x5
So this rule tells us that if we multiply two exponents with the same base then we just add the
exponents together.
Let's try another example:
22⋅24 = 22+4
= 26
= 2⋅2⋅2⋅2⋅2⋅2
= 64
Try these other examples on your own.
1. x15⋅x10
4. 103⋅105
2. x43⋅x54
5. x14y5⋅x11y9
3. 37⋅34