Lesson 8-2

Dividing Monomials

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 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.

A B C D

Solve the Test Item

• circumference of a circlelength of a square diameter of circle or 2rarea 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/an and 1/a-n = an

• Homework: – Pg. 421 14-36 even