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**Dividing and Reducing Monomials**

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**The Zero Power Rule Zero Property of Exponents**

A nonzero number to the zero power is 1:

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**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.).

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**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:

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**Quotient of Powers Rule**

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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.

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**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.

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**Power of a Quotient Rule**

For any numbers, a & b, and all integers m,

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