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Simplifying Expressions Using the Quotient of Powers Property

This guide provides step-by-step examples on how to simplify expressions using the Quotient of Powers Property. It covers techniques for subtracting exponents and emphasizes writing answers in power form. The guide also includes guided practice problems to reinforce understanding, enabling learners to gain proficiency in applying the property effectively when simplifying fractions with powers.

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Simplifying Expressions Using the Quotient of Powers Property

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  1. x12 a. x12 – 7 = x7 97 93 b. 97 – 3 = EXAMPLE 3 Using the Quotient of Powers Property Simplify the expression. Write your answer as a power. Quotient of powers property = x5 Subtract exponents. Quotient of powers property = 94 Subtract exponents.

  2. y4y a. = y3 b. xy4 – 3 = xy4 y5 y3 y3 EXAMPLE 4 Simplifying Fractions with Powers Simplify the expression. Simplify numerator using product of powers property. = y5 – 3 Quotient of powers property. = y2 Subtract exponents. Quotient of powers property. = xy Subtract exponents.

  3. a6 9. a4 109 106 10. for Examples 3 and 4 GUIDED PRACTICE Simplify the expression. Write your answer as a power. = a2 = 103

  4. q3 q5 11. q4 for Examples 3 and 4 GUIDED PRACTICE Simplify the expression. Write your answer as a power. = q4

  5. a2b8 12. b2 for Examples 3 and 4 GUIDED PRACTICE Simplify the expression. Write your answer as a power. = a2b6

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