Lesson 8.1
The Product Rule
When we multiply matching bases, we don't multiply the powers... we gather them up.
Introduction
We are entering the "Bridge" to Intermediate Algebra. This unit focuses on Exponents and Polynomials. The first rule is about what happens when you multiply two powers with the same base.
Past Knowledge
Lesson 1.4 (Exponents). You must know that .
Today's Goal
Simplify expressions like by adding the exponents.
Future Success
This is the foundation for Multiplying Polynomials (Lesson 8.6) and Scientific Notation.
Key Concepts
The Rule
If the bases are the same, ADD the exponents.
Why?
Worked Examples
Example 1: Basic Variables
BasicSimplify:
Check Bases
Both are . Good.
Add Exponents
Answer
Example 2: Coefficients vs. Exponents
IntermediateSimplify:
Multiply Numbers
Coefficients are normal numbers. Multiply them.
Add Powers
Exponents get added.
Answer
Example 3: Multiple Variables
AdvancedSimplify:
Coefficients
Variable A
Recall that plain is .
Variable B
Answer
Common Pitfalls
Multiplying Exponents
Students often multiply the exponents because they see a multiplication sign. NO! is , not .
Adding Coefficients
Students get so used to adding exponents that they add the big numbers too. is , not .
Real-Life Applications
Computer Memory:
- Computers deal with massive numbers of bits. is a Kilobyte. is a Megabyte.
- To calculate total memory, computer engineers strictly use exponent rules.
Practice Quiz
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