Warm Up Simplify. 1. 3. 5. (10²)³ 2. 4. 6.

Division Properties of Exponents Objective Use division properties of exponents to evaluate and simplify expressions.

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. Copy

Finding Quotients of Powers Simplify. A. B.

Finding Quotients of Powers Copy Finding Quotients of Powers Simplify. C. D.

Both and 729 are considered to be simplified. Helpful Hint

Try This! Simplify. a. b.

Try this! Simplify. c. d.

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. Copy

Finding Positive Powers of Quotient Simplify. Use the Power of a Quotient Property. Simplify.

Finding Positive Powers of Quotient Copy 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:

Finding Positive Powers of Quotient Copy 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: Use the Power of a Product Property:

Try This! Simplify. Use the Power of a Quotient Property. Simplify.

Try this! Simplify.

Try This! Simplify.

Copy

Finding Negative Powers of Quotients Copy Finding Negative Powers of Quotients Simplify. Rewrite with a positive exponent. Use the Powers of a Quotient Property . and

Finding Negative Powers of Quotients Simplify.

Finding Negative Powers of Quotients Copy Finding Negative Powers of Quotients Simplify. Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (3)2 (2n)3 = 32  23n3 and (2)2  (6m)3 = 22  63m3

Finding Negative Powers of Quotients Copy Finding Negative Powers of Quotients Simplify. Square and cube terms. 1 24 2 12 Divide out common factors. Simplify.

Whenever all of the factors in the numerator or the denominator divide out, replace them with 1. Helpful Hint

Try This! Simplify. Rewrite with a positive exponent. Use the power of a Quotient Property. 93=729 and 43 = 64.

Try This! Simplify. Rewrite with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Power Property: (b2c3)4= b2•4c3•4 = b8c12 and (2a)4= 24a4= 16a4.

Try This! Simplify. Rewrite each fraction with a positive exponent. Use the Power of a Quotient Property. Use the Power of a Product Property: (3)2= 9. Add exponents and divide out common terms.