# Glencoe Algebra 1 Over Lesson 71 Division Properties of Exponents Lesson 7-2 LEARNING GOAL

Understand how to divide monomials using properties of exponents and simplify expressions containing zero and negative exponents. VOCABULARY zero exponent any non-zero number raised to

the zero power equals 1. negative exponent for any real number a 0 and any integer n, order of magnitude the order of magnitude of a quantity is the number rounded to the nearest power of ten. Example: The order of magnitude of 45,000,000 is

. 45,000,000 is closest to 10,000,000. Quotient of Powers Group powers that have the same base.

Quotient of Powers = xy9 Simplify. Answer: xy9 Power of a Quotient Power of a Quotient

Power of a Product Power of a Power Answer: Simplify equal to zero.

Assume that p and q are not Zero Exponent A.

Answer: 1 Zero Exponent B. a0 = 1

Simplify. = nQuotient of Powers Answer: n A. Simplify zero.

. Assume that z is not equal to Negative Exponents A. Simplify . Assume that no denominator is

equal to zero. Negative Exponent Property Answer: Negative Exponents

B. Simplify . Assume that p, q and r are not equal to zero. Group powers with

the same base. Quotient of Powers and Negative Exponent Property Negative Exponents

Simplify. Negative Exponent Property Multiply. Answer:

A. Simplify equal to zero. . Assume that no denominator is 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 Darins account and Tabos account. How many orders of magnitude as great is Darins account as Tabos account? Understand

Plan We need to find the order of magnitude of the amounts of money in each account. Then find the ratio of Darins account to Tabos account. Round each dollar amount to the

nearest power of ten. Then find the ratio. Apply Properties of Exponents Solve

The amount in Darins account is close to \$100,000. So, the order is 105. The amount in Tabos account is close to 100, so the order of magnitude is 102. The ratio of Darins account to Tabos account is

or 103. 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. Apply Properties of Exponents

Check The ratio of Darins account to Tabos account is 792. The power of ten closest

to 792 is 1000, which has an order of magnitude of 103. 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. 101 B. 102 C. 103 D. 104 Homework p 403 #19-65 odd