lesson 8-2 dividing monomials. transparency 2 click the mouse button or press the space bar to...
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Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
Objectives
• Simplify exponents involving the quotient of monomials
• Simplify expressions containing negative exponents
Vocabulary
• Zero exponent – for any nonzero number a, a0 = 1
• Negative exponent – for any nonzero number a and any integer n, a-n = 1/an and 1/a-n = an
Laws of Exponents, Part 2
Division: (subtract exponents)
b6 b4 = b6-4 = b2
26 22 = 64 4 = 16 (= 24)
23 22 = 8 4 = 2 (= 21)
32 23 = 9 8 = 1.125 (bases not the same!)
Anything (except 0) raised to zero power = 1!
b0 = 1
32 32 = 9 9 = 1 (=30)
bbbbbb(bbbbbb) (bbbb) = ---------------------- = bb bbbb
(1256x2y8z3)0 = 1
Example 1
Simplify Assume 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 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.
A B C D
Solve the Test Item
• circumference of a circlelength of a square diameter of circle or 2rarea of square
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/an and 1/a-n = an
• Homework: – Pg. 421 14-36 even
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