1. § 1.6
Properties of Integral Exponents

2. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 1.6
Properties of Exponents
Exponent Rules
Product Rule
Quotient Rule
When multiplying exponential expressions with the
same base, add the exponents.
When dividing exponential expressions with
the same nonzero base, subtract the exponent
in the denominator from the exponent in the
numerator.
Blitzer, Intermediate Algebra, 5e – Slide #2 Section 1.6

3. Blitzer, Intermediate Algebra, 5e – Slide #3 Section 1.6
Properties of Exponents
Exponent Rules
Examples
Product Rule
Quotient Rule
Blitzer, Intermediate Algebra, 5e – Slide #3 Section 1.6

4. Blitzer, Intermediate Algebra, 5e – Slide #4 Section 1.6
Properties of Exponents
The Zero Exponent Rule:
If b is any real number other than 0, then
Negative Exponent Rule: If b is any real number other than 0 and n is a natural number, then
and
Blitzer, Intermediate Algebra, 5e – Slide #4 Section 1.6

5. Properties of Exponents
Exponent Rules
Examples
Zero Exponent Rule
Negative Exponent Rule
Blitzer, Intermediate Algebra, 5e – Slide #5 Section 1.6

6. Properties of Exponents
Exponent Rules
Examples
Negative Exponents in Numerators and Denominators
Power Rule
Blitzer, Intermediate Algebra, 5e – Slide #6 Section 1.6

7. Blitzer, Intermediate Algebra, 5e – Slide #7 Section 1.6
Properties of Exponents
Exponent Rules
Examples
Products to Powers
Quotients to Powers
Blitzer, Intermediate Algebra, 5e – Slide #7 Section 1.6

8. Simplification Techniques
Simplifying Exponential Expressions
Simplification Techniques
Examples
If necessary, remove parentheses by using the Products to Powers Rule or the Quotient to Powers Rule.
If necessary, simplify powers to powers by using the Power Rule.
Blitzer, Intermediate Algebra, 5e – Slide #8 Section 1.6

9. Simplification Techniques
Simplifying Exponential Expressions
Simplification Techniques
Examples
Be sure each base appears only once in the final form by using the Product Rule or Quotient Rule
If necessary, rewrite exponential expressions with zero powers as 1. Furthermore, write the answer with positive exponents by using the Negative Exponent Rule
Blitzer, Intermediate Algebra, 5e – Slide #9 Section 1.6

10. Blitzer, Intermediate Algebra, 5e – Slide #10 Section 1.6
Properties of Exponents
Of I M P O R T A N CE to note…
Be sure you pay special attention to the study tip on the bottom of page 72. This tip will help you avoid common errors that can occur when simplifying exponential expressions.
Blitzer, Intermediate Algebra, 5e – Slide #10 Section 1.6