1. Dividing Monomials

2. Quotient of Powers
Look for a pattern in the exponents.
Definition of Power 1 1 1
Cancel common factors. 4 4 4 4 4 4 4 42 42
_____________________
_______
____ = = = = 4 4 4 1
What is the pattern? 1 1 1 1
KEY CONCEPT Quotient of Powers
To divide two powers with the same base, subtract their exponents.

3. Simplify
Group powers that have the same base.
Divisions of Powers
Simplify
A variable with no exponent indicated can be written as a power of 1.

4. Simplify Simplify Group powers that have the same base.
Quotient of Powers
Simplify

5. Simplify Simplify Group powers that have the same base.
Quotient of Powers
Simplify

6. Power of a Quotient KEY CONCEPT Power of a Quotient
Definition of Power
Look for a pattern in the exponents.
Multiply
3 factors
What is the pattern?
3 factors
KEY CONCEPT Power of a Quotient
To find a power of a quotient, find the power of the numerator and the power of the denominator.

7. Any number raised to the zero power is equal to 1.
The Zero Exponent
Simplify
Definition of Power
Cancel common factors.
Method 1
Method 2
Quotient of Powers
KEY CONCEPT Zero Exponent
Any number raised to the zero power is equal to 1.

8. Simplify Remember anything to the zero power is equal to 1
Definition of Zero Exponent.
Remember anything to the zero power is equal to 1
Even an entire expression raised to the zero power equals 1!

9. Simplify
Zero Exponent
Quotient of Powers

10. Negative Exponents KEY CONCEPT Negative Exponent
Simplify
Definition of Power
Cancel common factors.
Method 1
Method 2
Quotient of Powers
KEY CONCEPT Negative Exponent
For any nonzero number a and any integer n, a-n is the reciprocal of an. In addition, the reciprocal of a-n is an.

11. Negative Exponents Definition
Simplify
Write as a product of fractions.
Negative Exponents Definition

12. Negative Exponents Definition
Simplify
Write as a product of fractions.
Negative Exponents Definition
Multiply Fractions

13. Simplify Write as a product of fractions.
Quotient of Powers and Negative Exponent Definition
Simplify
Negative Exponent and Zero Exponent Definitions
Multiply

14. Negative Exponent Definition
Simplify
Write as a product of fractions.
Quotient of Powers
Simplify
Negative Exponent Definition
Multiply