8-2 Dividing Monomials Objectives Students will be able to: 1)Simplify expressions involving the quotient of monomials 2)Simplify expressions containing negative exponents

Let’s discover the rule for dividing monomials. Write out the following quotients in expanded form. Then simplify. See if you can discover a rule.

Rules for Dividing Monomials Quotient of Powers: when dividing two powers with the same base, subtract the exponents Power of a Quotient: when a quotient is raised to a power, raise both the numerator and denominator to that power

Simplify the quotient. 1) 2) 3)

4)5) 6)

Try these. 7)8) 9)10)

Negative Exponents An expression is not simplified if it contains negative exponents. Simplify this expression by first writing it out in expanded form:

When a term in the numerator contains a negative exponent, bring that term down to the denominator to make the exponent positive. When a term in the denominator contains a negative exponent, bring that term up to the numerator to make the exponent positive.

Simplify. 1)2) 3)4)

5)6)

Try these. 7)8) 9)10)

11)12)

Try these. 13)14)

Let’s look at what we would do when an entire quotient is raised to a negative exponent… When an entire quotient is raised to a negative exponent, take the reciprocal of the fraction and then change the exponent to a positive.

Simplify. 1) 2)

3)

Try these. 4)5)