1. Dividing and Reducing Monomials

2. The Zero Power Rule Zero Property of Exponents
A nonzero number to the zero power is 1:

3. Quotient of Powers Simplify the following expression:
Step 1: Write out the expressions in expanded form.
Step 2: Cancel matching factors (A factor is a term that is multiplied by the rest of the expression; here, ‘a’ is a factor.).

4. Quotient of Powers Rule
Let’s look at the results:
Notice:
• the base is still ‘a’.
• the power is 2 = (7 - 5).
• the term that didn’t cancel is in the numerator (where the larger power was to begin with).
For all values, a, and all integers m and n:

5. Quotient of Powers Rule

6. Dividing Monomials
These monomials have coefficients and more than one variable. Reduce the coefficients as you would with a typical fraction and use the power rule for the variables.

7. Power of a Quotient Simplify the following:
Step 1: Distribute the power to both the numerator & denominator.
Step 2: Find the powers of the numerator & denominator.
Step 3: Reduce if you can.

8. Power of a Quotient Rule
For any numbers, a & b, and all integers m,