7 4 Division Properties of Exponents Lesson Objective

7 -4 Division Properties of Exponents Lesson Objective: I will be able to … • Use division properties of exponents to evaluate and simplify expressions Language Objective: I will be able to … • Read, write, and listen about vocabulary, key concepts, and examples Holt Algebra 1

7 -4 Division Properties of Exponents A quotient of powers with the same base can be found by writing the powers in a factored form and dividing out common factors. Notice the relationship between the exponents in the original quotient and the exponent in the final answer: 5 – 3 = 2. Holt Algebra 1

7 -4 Division Properties of Exponents Page 16 Holt Algebra 1

7 -4 Division Properties of Exponents Page 17 Example 1: Finding Quotients of Powers Simplify. A. B. Holt Algebra 1 C.

7 -4 Division Properties of Exponents Helpful Hint Both Holt Algebra 1 and 729 are considered to be simplified.

7 -4 Division Properties of Exponents Page 18 Simplify. Holt Algebra 1 Your Turn 1

7 -4 Division Properties of Exponents Example 2: Dividing Numbers in Page 18 Scientific Notation Simplify and write the answer in scientific notation Holt Algebra 1

7 -4 Division Properties of Exponents Writing Math You can “split up” a quotient of products into a product of quotients: This is not true for addition and subtraction! Holt Algebra 1

7 -4 Division Properties of Exponents Page 19 Your Turn 2 Simplify and write the answer in scientific notation. Holt Algebra 1

7 -4 Division Properties of Exponents Page 19 Example 3: Economic Application The Colorado Department of Education spent about dollars in fiscal year 2004 -05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form. To find the average spending per student, divide the total debt by the number of students. = 0. 58 × 109– 5 = 0. 58 × 104 = $5800 Holt Algebra 1

7 -4 Division Properties of Exponents A power of a quotient can be found by first writing the numerator and denominator as powers. Notice that the exponents in the final answer are the same as the exponent in the original expression. Holt Algebra 1

7 -4 Division Properties of Exponents Page 16 Holt Algebra 1

7 -4 Division Properties of Exponents Page 20 Example 4: Finding Positive Powers of Quotient Simplify. A. Holt Algebra 1 B.

7 -4 Division Properties of Exponents Page 20 Simplify. Holt Algebra 1 Your Turn 4

7 -4 Division Properties of Exponents Remember that Therefore, Holt Algebra 1 . What if x is a fraction? .

7 -4 Division Properties of Exponents Page 17 Holt Algebra 1

7 -4 Division Properties of Exponents Page 21 Simplify. Holt Algebra 1 Example 5: Finding Negative Powers of Quotients

7 -4 Division Properties of Exponents Page 21 Simplify. Holt Algebra 1 Your Turn 5

7 -4 Division Properties of Exponents Classwork Assignment #3 • Holt 7 -4 #3 – 5, 8 – 10, 14 – 16 Holt Algebra 1

7 -4 Division Properties of Exponents Homework Assignment #3 • Holt 7 -3 #19 – 40, 41 – 51 odd, 54 – 58 • Holt 7 -4 #19 – 22, 25 – 45 odd • KIN 7 -5 and 7 -6 Holt Algebra 1