1. Dividing Monomials: The Quotient Rule and Integer Exponents
5 Section 4
Dividing Monomials: The Quotient Rule and Integer Exponents

2. Section 5.4 Objectives
1 Simplify Exponential Expressions Using the Quotient Rule
2 Simplify Exponential Expressions Using the Quotient to a Power Rule
3 Simplify Exponential Expressions Using Zero as an Exponent
4 Simplify Exponential Expressions Involving Negative Exponents
5 Simplify Exponential Expressions Using the Laws of Exponents

3. The Quotient Rule a.) b.) The Quotient Rule for Exponents
If a is a real number and if m and n are positive integers, then
Example: Simplify each expression.
Remember that the base does not change.
a.)
b.)

4. The Quotient to a Power Rule
Quotient to a Power Rule for Exponents
if b  0.
Example: Simplify each expression:
a.)
b.)

5. Zero Exponent
If a is a nonzero real number (that is, a  0), we define
a0 = 1
Example: Simplify each expression.
a.)
b.)

6. Negative Exponent
If n is a positive integer and if a is a nonzero real number (that is, a  0), then we define
Example: Simplify each expression.
a.)
b.)

7. Negative Exponent
If a and b are real numbers and n is an integer, then
if a  0, b  0
Example: Simplify each expression.
a.)
b.)

8. Simplifying Expressions
Example: Simplify the expression:
Rearrange factors.
Find each product.
Simplify.

9. Simplifying Expressions
How to Simplify Expressions Using the Quotient Rule and
the Negative Exponent Rule
Step 1: Write the quotient as the product of factors.
Step 2: Find each quotient.
Step 3: Simplify. Write the quotient so that the exponents are positive.
Example: Simplify the expression:
Write the quotient as products.
Find each quotient.
Simplify.

10. Simplifying Expressions
How to Simplify Expressions Using the Power Rule and
the Negative Exponent Rule
Step 1: Write the quotient as the product of factors.
Step 2: Find each product.
Step 3: Simplify. Write the product so that the exponents are positive.
Example: Simplify the expression:
Write the quotient as products.
Find each product.
Simplify.