Lesson 8-2 Dividing Monomials. Transparency 2 Click the mouse button or press the Space Bar to...
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Transcript of Lesson 8-2 Dividing Monomials. Transparency 2 Click the mouse button or press the Space Bar to...
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