1. Sections 8-3, 8-4, & 8-5 Properties of Exponents SPI 11D: use exponents to simplify a monomial written in expanded form
Objectives:
Apply the rules of exponents
Vocabulary
Monomial:
an algebraic expression consisting of only one term
Example of some monomials: 12, y, -5x2y, ½x2
Exponent:
a quantity representing the power to which some other quantity is raised
shorthand way to show products of like factors
2 • 2 • 2 = Exponent
Factors Base

2. which means Example Property of Exponents
Multiplying powers with the Same Base
For every non-zero number a and integers m and n,
am ∙ an = a m + n
which means
If multiplying terms with like bases, add the exponents.
Example
Rewrite each expression using exponents.

3. Property of Exponents
When terms have more than one base, combine only those powers with the same base
Simplify each expression.

4. which means Property of Exponents Negative Exponents
Always remove negative signs from the exponents
For every non-zero number a and integer n,
which means
If term with negative exponent is on top, put on bottom and remove negative sign from exponent, and vice versa.
Simplify each expression:

5. Raising a Power to a Power
Property of Exponents
Raising a Power to a Power
Always remove negative signs from the exponents
For every non-zero number a and integers m and n,
Simplify each expression:

6. Raising a Product to a Power
Property of Exponents
Raising a Product to a Power
Always remove negative signs from the exponents
For every non-zero number a and integer n,
Simplify each expression:

7. which means Example Property of Exponents
Dividing powers with the Same Base
For every non-zero number a and integers m and n,
which means
If dividing terms with like bases, subtract the exponents.
Example
Simplify each expression

8. Multiplying Numbers in Scientific Notation
Property of Exponents
Multiplying Numbers in Scientific Notation
Scientific Notation:
shorthand to write very large or very small numbers
written in the form with base of 10
all the exponent rules apply
Simplify the expression and write in scientific notation.

9. Exponents and Physical Science
An object has a mass of 102 kg. The expression
102 • (3  108)2 describes the amount of resting energy in joules the object contains. Simplify the expression and write in scientific notation.
102 • (3  108)2 = 102 • 32 • (108)2
= 102 • 32 • 1016
= 32 • 102 • 1016
= 32 •
= 9  1018