Division properties of exponents Section 7.2

7.2 Topic Focus I can divide monomials using the properties of exponents I can simplify expressions containing negative and zero exponents

Main Question Discovery Expand and evaluate the following 2 7 2 4 𝑥 4 𝑥 3

Quotient of Powers Definition 𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚−𝑛

Use the Quotient of Powers property to simplify the following: 𝑔 3 ℎ 5 𝑔 ℎ 2 𝑥 3 𝑦 4 𝑥 2 𝑦 𝑘 7 𝑚 10 𝑝 𝑘 5 𝑚 3 𝑝

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Main Question Discovery Expand and evaluate the following 3 4 3 𝑐 2 𝑑 2

Power of a Quotient Definition 𝑎 𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚

Use the Power of a Quotient property to evaluate the following: 3 𝑝 3 7 2 4 𝑥 3 5 𝑦 4 3 5 𝑥 5 𝑦 6𝑧 2

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Main Question Discovery Use the Quotient of Powers property to evaluate 3 5 3 5 Expand and evaluate 3 5 3 5

Zero Exponent Property Definition 𝑎 0 =1

Use the Zero Exponent Property to simplify the following: 𝑥 5 𝑦 0 𝑥 3 𝑏 4 𝑐 2 𝑑 0 𝑏 2 𝑐 12 𝑚 8 𝑛 7 8 𝑚 5 𝑛 10 0

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Main Question Discovery Use the Quotient of Powers property to evaluate 𝑐 2 𝑐 5 Expand and evaluate 𝑐 2 𝑐 5

Negative Exponent Property Definition 𝑎 −𝑚 = 1 𝑎 𝑚

Use the Negative Exponent Property to simplify the following: 2 −4 1 𝑥 −3

Use all multiplication and division properties to simplify the following: 𝑛 −5 𝑝 4 𝑟 −2 𝑣 −3 𝑤 𝑥 2 𝑤 𝑦 −6 3 𝑎 2 𝑏 −5 𝑐 3 −9 𝑎 7 𝑏 −2 𝑐 −3

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Team Points Challenge #1 Simplify 5 𝑟 −3 𝑡 4 −20 𝑟 2 𝑡 7 𝑢 5

Team Points Challenge #2 Simplify −10 𝑎 2 𝑏 3 𝑐 −5 2 𝑎 −3 𝑏 −1 𝑐 −4

Team Points Challenge #3 Simplify 2 𝑥 2 𝑦 4 −1 5 𝑥 −2 𝑦 −7