1. Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Chapter P
Prerequisites:
Fundamental Concepts of Algebra
P.2 Exponents and
Scientific Notation
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1

2. Objectives:
Use the product rule.
Use the quotient rule.
Use the zero-exponent rule.
Use the negative-exponent rule.
Use the power rule.
Find the power of a product.
Find the power of a quotient.
Simplify exponential expressions.
Use scientific notation.

3. The Product Rule
When multiplying exponential expressions with the same base, add the exponents. Use this sum as the exponent of the common base.

4. Example: Using the Product Rule
Multiply the expression using the product rule:

5. The Quotient Rule
When dividing exponential expressions with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator. Use this difference as the exponent of the common base.

6. Example: Using the Quotient Rule
Divide using the quotient rule:

7. The Zero-Exponent Rule
If b is any real number other than 0,

8. Example: Using the Zero-Exponent Rule
Simplify:

9. The Negative Exponent Rule
If b is any real number other than 0 and n is a natural number, then

10. Example: Using the Negative-Exponent Rule
Use the negative-exponent rule to write with a positive exponent.
Answer:
Use the negative-exponent rule to write with positive exponents only.

11. The Power Rule (Powers to Powers)
When an exponential expression is raised to a power, multiply the exponents. Place the product of the exponents on the base and remove the parentheses.

12. Example: Using the Power Rule (Powers to Powers)
Simplify the expression using the power rule:

13. The Products-to-Powers Rule for Exponents
When a product is raised to a power, raise each factor to that power.

14. Example: Raising a Product to a Power
Simplify:

15. The Quotients-to-Powers Rule for Exponents
When a quotient is raised to a power, raise the numerator to that power and divide by the denominator to that power.
If b is a nonzero real number, then

16. Example: Raising Quotients to Powers
Simplify:

17. Simplifying Exponential Expressions
An exponential expression is simplified when:
No parentheses appear.
No powers are raised to powers.
Each base occurs only once.
No negative or zero exponents appear.

18. Example: Simplifying Exponential Expressions

19. Scientific Notation
A number is written in scientific notation when it is expressed in the form
where the absolute value of a is greater than or equal to 1 and less than 10, and n is an integer.

20. Example: Converting from Decimal Notation to Scientific Notation
Write in scientific notation:
5,210,000,000 –