# Dividing and Reducing Monomials

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Dividing and Reducing Monomials

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

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.).

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:

Quotient of Powers Rule

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.

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.

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