LESSON 7–2 Division Properties of Exponents

Lesson Menu Five-Minute Check (over Lesson 7–1) TEKS Then/Now New Vocabulary Key Concept: Quotient of Powers Example 1: Quotient Powers Key Concept: Power of a Quotient Example 2: Power of a Quotient Key Concept: Zero Exponent Property Example 3: Zero Exponent Key Concept: Negative Exponent Property Example 4: Negative Exponents Example 5: Real-World Example: Apply Properties of Exponents

Over Lesson 7–1 5-Minute Check 1 A.Yes, the expression is a product of a number and variables. B.No, it has a variable. Determine whether –5x 2 is a monomial. Explain your reasoning.

Over Lesson 7–1 5-Minute Check 2 A.Yes, the exponents are the same power. B.No, the expression is the difference between two powers of variables. Determine whether x 3 – y 3 is a monomial. Explain your reasoning.

Over Lesson 7–1 5-Minute Check 3 A.3a 5 b 6 B.–3a 5 b 6 C.3a 3 b 2 D.9a 3 b 6 Simplify (3ab 4 )(–a 4 b 2 ).

Over Lesson 7–1 5-Minute Check 4 A.2x 7 y 6 B.2x 10 y 8 C.4x 10 y 8 D.4x 7 y 6 Simplify (2x 5 y 4 ) 2.

Over Lesson 7–1 5-Minute Check 5 Find the area of the parallelogram. A. B.10n 5 C.5n 6 D.5n 5 units 2

Over Lesson 7–1 5-Minute Check 6 A.20x 5 y 3 z 6 B.20x 6 y 3 z 8 C.51x 5 y 3 z 6 D.51x 6 y 3 z 8 What is the product (–3x 2 y 3 z 2 )(–17x 3 z 4 )?

TEKS Targeted TEKS A.11(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents. Mathematical Processes A.1(E), A.1(G)

Then/Now You multiplied monomials using the properties of exponents. Divide monomials using the properties of exponents. Simplify expressions containing negative and zero exponents.

Vocabulary zero exponent negative exponent order of magnitude

Concept

Example 1 Quotient of Powers Group powers that have the same base. = xy 9 Simplify. Quotient of Powers Answer: xy 9

Example 1 A. B. C. D.

Concept

Example 2 Power of a Quotient Power of a Power Power of a Product Answer:

Simplify Assume that p and q are not equal to zero. Example 2 A.AnsA B.AnsB C.AnsC D.AnsD

Concept

Example 3 Zero Exponent Answer: 1 A.

Example 3 Zero Exponent B. a 0 = 1 = nQuotient of Powers Simplify. Answer: n

Example 3 A. B.1 C.0 D.–1 A. Simplify. Assume that z is not equal to zero.

Example 3 A. B. C. D. B. Simplify. Assume that x and k are not equal to zero.

Concept

Example 4 Negative Exponents Negative Exponent Property A. Simplify. Assume that no denominator is equal to zero. Answer:

Example 4 Negative Exponents Group powers with the same base. Quotient of Powers and Negative Exponent Property

Example 4 Negative Exponents Negative Exponent Property Multiply. Simplify. Answer:

Example 4 A. Simplify. Assume that no denominator is equal to zero. A. B. C. D.

Example 4 A.AnsA B.AnsB C.AnsC D.AnsD B. Simplify. Assume that no denominator is equal to zero.

Example 5 Apply Properties of Exponents SAVINGS Darin has $123,456 in his savings account. Tabo has $156 in his savings account. Determine the order of magnitude of Darin’s account and Tabo’s account. How many orders of magnitude as great is Darin’s account as Tabo’s account? AnalyzeWe need to find the order of magnitude of the amounts of money in each account. Then find the ratio of Darin’s account to Tabo’s account. FormulateRound each dollar amount to the nearest power of ten. Then find the ratio.

Example 5 Apply Properties of Exponents DetermineThe amount in Darin’s account is close to $100,000. So, the order is The amount in Tabo’s account is close to 100, so the order of magnitude is The ratio of Darin’s account to Tabo’s account is or Answer:So, Darin has about 1000 times as much as Tabo, or Darin has 3 orders of magnitude as much in his account as Tabo.

JustifyThe ratio of Darin’s account to Tabo’s account is ≈ 792. The power of ten closest to 792 is 1000, which has an order of magnitude of  Example 5 Apply Properties of Exponents Evaluate Rounding and analyzing the orders of magnitude of a solution is an effective tool to determine the reasonableness of a solution. Our solution is reasonable because the actual savings ratio rounds to the order of magnitude.

Example 5 A circle has a radius of 210 centimeters. How many orders of magnitude as great is the area of the circle as the circumference of the circle? A.10 1 B.10 2 C.10 3 D.10 4

LESSON 7–2 Division Properties of Exponents