Objective 1: To multiply monomials. Objective 2: To divide monomials and simplify expressions with negative exponents.

To multiply monomials

Exponent Review Base Exponent

It means to use 2 as a factor 5 times. What does it mean?

Exponent Review Base Exponent

What does it mean?

Multiplying with exponents When you multiply, add the exponents.

Example 1 What’s the exponent for this x?

Example 1 Multiply the coefficients first.

Example 1

Example 2

Raising a power to a power When raising a power to another power, multiply the exponents.

Raising a power to a power When raising a power to another power, multiply the exponents. Take everything in parentheses and raise it to the 2 nd power.

Raising a power to a power When raising a power to another power, multiply the exponents. Use Distributive Property.

Example 3 Simplify the coefficient.

Example 3

Example 4 What’s the exponent for this x?

Example 4 Simplify this expression first because it has an outside exponent. Take everything in parentheses and raise it to the 3 rd power.

Example 4 Now, there are no outside exponents. We can multiply the coefficients Then multiply the x’s Then multiply the y’s

Example 4

Example 5 (skip) Start outside the brackets Multiply the two outside exponents.

Example 5 Simplify the outside exponent. Raise everything inside the parentheses to the 6 th power.

Example 5

To divide monomials and simplify negative exponents.

Dividing with exponents When you divide, subtract the exponents.

Example 6 What’s the exponent for this b?

Example 6

Example 7 Raise everything in the parentheses to the 2 nd power.

Example 7 Subtract the exponents.

Example 7

Example 8 Raise everything in the parentheses to the 3 rd power.

Example 8 Simplify the denominator.

Example 8

Look At This

This is another rule.

Zero as exponent Anything raised to zero power equals 1.

Review: Whole Numbers Any whole number can be placed on top of 1.

Review: Whole Numbers Any whole number can be placed on top of 1.

Review: Whole Numbers Any whole number can be placed on top of 1.

Review: Whole Numbers Any whole number can be placed on top of 1.

Review: Whole Numbers Any whole number can be placed on top of 1.

Review: Whole Numbers Any whole number can be placed on top of 1.

Fractions There are 2 parts of a fraction.

Negative Exponents When you see negative exponents, think MOVE & CHANGE Move the base from top to bottom or bottom to top. Change the exponent to a positive number.

Negative Exponents MOVE & CHANGE

Negative Exponents MOVE & CHANGE

Negative Exponents MOVE & CHANGE y does not have negative exponent. It stays where it is. Nothing is left on top. We know there is an invisible 1 there.

Negative Exponents

MOVE & CHANGE

Negative Exponents MOVE & CHANGE

Negative Exponents MOVE & CHANGE

Negative Exponents MOVE & CHANGE

Example 9 Raise everything in the parentheses to the negative 2 nd power.

Example 9 Move the negative exponents and change to positive exponents.

Example 9

Example 10

Example 11 Move any negative exponents and change to positive.

Example 11

Example 12 (skip) Subtract the exponents.

Example 12 Put under 1 and change exponent to positive.

Example 12 The variable stays where the bigger exponent was.

IMPORTANT! Your final answer can NOT have any negative exponents. Remember to move all negative exponents and change them to positives.

All Rules in Symbolic Form

Example 13

Move negative exponents and change to positive.

Example 13

Example 14

Move negative exponents and change to positive.

Example 14