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Published byLionel Ray Modified over 9 years ago
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Lesson Menu
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Over Lesson 7–2 5-Minute Check 1
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Splash Screen Rational Exponents Lesson 7-3
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Then/Now Understand how to rewrite and evaluate expressions involving rational exponents and solve equations containing rational expressions.
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Vocabulary
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Concept
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Example 1A Radical and Exponential Forms Answer: 9 Write each expression in radical form, or write each radical in exponential form. = 9Simplify.
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Example 1B Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form.
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Example 1CYP
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Concept
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Example 2A nth Roots A. B. C.
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Concept
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Example 3 Evaluate b Expressions Answer: 11 A. = 11Simplify.
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Example 3 Evaluate b Expressions Answer: 7 = 7Simplify. B.
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Example 3
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Concept
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Example 4A Evaluate b Expressions Answer: 4 = 2 2 2 5 = 32 = 4Simplify.
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Example 4B Evaluate b Expressions Answer: 59,049 = 9 5 9 2 = 81 = 59,049Simplify.
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Example 4
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Concept
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Example 5A Solve Exponential Equations A. Solve 9 x = 729. Answer:3 9 x = 729Original equation 9 x = 9 3 Rewrite 729 as 9 3. x= 3Power Property of equality
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Example 5B Solve Exponential Equations B. Solve 16 2x – 1 = 8. 16 2x – 1 = 8 Original equation (2 4 ) 2x – 1 = 2 3 Rewrite 16 as 2 4 and 8 as 2 3. 2 8x – 4 = 2 3 Power of a Power, Distributive Property 8x – 4= 3Power Property of Equality 8x = 7Add 4 to each side. Divide each side by 8. Answer:
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Example 5A Solve 93 x + 1 = 27 4.
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Example 6 BIOLOGY The population p of a culture that begins with 40 bacteria and doubles every 8 hours can be modeled by, where t is time in hours. Find t if p = 20,480. Original equation p = 20,480 Divide each side by 40. Solve Exponential Equations
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Example 6 Solve Exponential Equations Rewrite 512 as 2 9. 72= tMultiply each side by 8. Power Property of Equality Answer:72
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Example 6 NEWS The number of hits to a news story online can be modeled by, where t is time in hours. Find t if h = 24,576.
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End of the Lesson Homework p
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