Lesson 8-2 Dividing Monomials

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Objectives Simplify exponents involving the quotient of monomials Simplify expressions containing negative exponents

Vocabulary Zero exponent – for any nonzero number a, a 0 = 1 Negative exponent – for any nonzero number a and any integer n, a -n = 1/a n and 1/a -n = a n

Laws of Exponents, Part 2 Division: (subtract exponents) b 6  b 4 = b 6-4 = b  2 2 = 64  4 = 16 (= 2 4 ) 2 3  2 2 = 8  4 = 2 (= 2 1 ) 3 2  2 3 = 9  8 = (bases not the same!) Anything (except 0) raised to zero power = 1! b 0 =  3 2 = 9  9 = 1 (=3 0 ) b  b  b  b  b  b (b  b  b  b  b  b)  (b  b  b  b) = = b  b b  b  b  b (1256x 2 y 8 z 3 ) 0 = 1

Example 1 SimplifyAssume that x and y ≠ 0. Quotient of Powers Group powers that have the same base. Answer: Simplify.

Example 2 Simplify Assume that e and f ≠ 0. Power of a Quotient Power of a Product Power of a PowerAnswer:

Example 3a Simplify Assume that m and n ≠ 0. Answer: 1

Example 3b Simplify. Assume that m and n ≠ 0. Simplify. Answer: Quotient of Powers

Example 4a Simplify. Assume that y and z ≠ 0. Write as a product of fractions. Answer: Multiply fractions.

Example 4b Simplify. Assume that p, q, and r ≠ 0. Group powers with the same base. Quotient of Powers and Negative Exponent Properties Simplify. Multiply fractions. Answer: Negative Exponent Property

Example 5 Read the Test Item A ratio is a comparison of two quantities. It can be written in fraction form. Multiple-Choice Test Item Write the ratio of the circumference of the circle to the area of the square in simplest form. AB CD Solve the Test Item circumference of a circle length of a square diameter of circle or 2r area of square

Example 5 cont Substitute. Quotient of Powers Simplify. Answer: C

Summary & Homework Summary: –To divide two powers with the same base, subtract the exponents –To find the power of a quotient, find the power of the numerator and the power of the denominator –Any nonzero number raised to the zero power is 1 –For any nonzero number a and any integer n, a -n = 1/a n and 1/a -n = a n Homework: –Pg even