8.5 Dividing Exponents

8.5 – Dividing Exponents Warm Up Simplify. 1. (x2)3 3. 5. 2. 4. 6. Write in Scientific Notation. 7. 8.

8.5 – Dividing Exponents Objective Use division properties of exponents to evaluate and simplify expressions.

8.5 – Dividing 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.

8.5 – Dividing Exponents

8.5 – Dividing Exponents When we multiply exponents with the same base ADD the exponents! When we divide exponents with the same base SUBTRACT the exponents!!! 5 4 5 4 4 + 4 5 8 = 5 = * 5 6 2 5 6 - 2 5 4 = =

Example 1: Finding Quotients of Powers 8.5 – Dividing Exponents Example 1: Finding Quotients of Powers Simplify. A. B.

Example 1: Finding Quotients of Powers 8.5 – Dividing Exponents Example 1: Finding Quotients of Powers Simplify. C. D.

8.5 – Dividing Exponents Check It Out! Example 1 Simplify. a. b.

8.5 – Dividing Exponents Check It Out! Example 1 Simplify. c. d.

8.5 – Dividing Exponents Simplify: 6 a 14 a

8.5 – Dividing Exponents Simplify: -1 3 c d 5 - 4 c d

8.5 – Dividing Exponents Simplify: 4 b 9 b

8.5 – Dividing Exponents Simplify: 10 z 5 z

Example 2: Dividing Numbers in Scientific Notation 8.5 – Dividing Exponents Example 2: Dividing Numbers in Scientific Notation Simplify and write the answer in scientific notation Write as a product of quotients. Simplify each quotient. Simplify the exponent. Write 0.5 in scientific notation as 5 x 10 . The second two terms have the same base, so add the exponents. Simplify the exponent.

8.5 – Dividing Exponents Example 3: Application The Michigan Department of Education spent about dollars in fiscal year 2010-11 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. Write as a product of quotients.

8.5 – Dividing Exponents Example 3 Continued The Michigan Department of Education spent about dollars in fiscal year 2010-11 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. Simplify each quotient. Simplify the exponent. Write in standard form. The average spending per student is $5,800.

( ) 8.5 – Dividing Exponents What happens if we have an expression like this? ( ) 3 4 2 x

8.5 – Dividing 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.

8.5 – Dividing Exponents

Example 4A: Finding Positive Powers of Quotient 8.5 – Dividing Exponents Example 4A: Finding Positive Powers of Quotient Simplify. Use the Power of a Quotient Property. Simplify.

Example 4B: Finding Positive Powers of Quotient 8.5 – Dividing Exponents Example 4B: Finding Positive Powers of Quotient Simplify. Use the Power of a Product Property. Use the Power of a Product Property: Simplify and use the Power of a Power Property:

Example 4C: Finding Positive Powers of Quotient 8.5 – Dividing Exponents Example 4C: Finding Positive Powers of Quotient Simplify. Use the Power of a Product Property. Use the Power of a Product Property: Use the Power of a Product Property:

8.5 – Dividing Exponents Example 4C Continued Simplify. Use the Power of a Product Property:

8.5 – Dividing Exponents Check It Out! Example 4a Simplify. Use the Power of a Quotient Property. Simplify.

8.5 – Dividing Exponents Check It Out! Example 4b Simplify.

8.5 – Dividing Exponents Check It Out! Example 4c Simplify.

8.5 – Dividing Exponents Simplify ( ) 2 3 2 x

8.5 – Dividing Exponents Simplify ( ) 3 x 2 y

8.5 – Dividing Exponents Simplify ( ) - 2 3 5

Example 5A: Finding Negative Powers of Quotients 8.5 – Dividing Exponents Example 5A: Finding Negative Powers of Quotients Simplify. Rewrite with a positive exponent. Use the Powers of a Quotient Property . and

Example 5B: Finding Negative Powers of Quotients 8.5 – Dividing Exponents Example 5B: Finding Negative Powers of Quotients Simplify.

8.5 – Dividing Exponents 1. 3. 4. 5. Lesson Quiz: Part I Simplify. 2.