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

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**Division Properties of Exponents**

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

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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

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**Finding Quotients of Powers**

Simplify. A. B.

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**Finding Quotients of Powers**

Copy Finding Quotients of Powers Simplify. C. D.

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**Both and 729 are considered to be simplified.**

Helpful Hint

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Try This! Simplify. a. b.

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Try this! Simplify. c. d.

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**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

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**Finding Positive Powers of Quotient**

Simplify. Use the Power of a Quotient Property. Simplify.

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**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:

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**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:

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

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Try this! Simplify.

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Try This! Simplify.

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Copy

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**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

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**Finding Negative Powers of Quotients**

Simplify.

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**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

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**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.

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

Helpful Hint

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

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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.

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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.

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