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Lesson 8-2 Dividing Monomials
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Transparency 2 Click the mouse button or press the Space Bar to display the answers.
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Objectives Simplify exponents involving the quotient of monomials Simplify expressions containing negative exponents
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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
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Laws of Exponents, Part 2 Division: (subtract exponents) b 6 b 4 = b 6-4 = b 2 2 6 2 2 = 64 4 = 16 (= 2 4 ) 2 3 2 2 = 8 4 = 2 (= 2 1 ) 3 2 2 3 = 9 8 = 1.125 (bases not the same!) Anything (except 0) raised to zero power = 1! b 0 = 1 3 2 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
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Example 1 SimplifyAssume that x and y ≠ 0. Quotient of Powers Group powers that have the same base. Answer: Simplify.
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Example 2 Simplify Assume that e and f ≠ 0. Power of a Quotient Power of a Product Power of a PowerAnswer:
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Example 3a Simplify Assume that m and n ≠ 0. Answer: 1
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Example 3b Simplify. Assume that m and n ≠ 0. Simplify. Answer: Quotient of Powers
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Example 4a Simplify. Assume that y and z ≠ 0. Write as a product of fractions. Answer: Multiply fractions.
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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
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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
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Example 5 cont Substitute. Quotient of Powers Simplify. Answer: C
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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. 421 14-36 even
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