Power Up 5 Copyright © 2026 Pearson Education, Inc. Power Up (50 – 60 minutes) Learning Objective(s): Students will convert between radical and rational exponent notation. Students will evaluate numerical expressions involving rational exponents. Students will apply the laws of exponents to generate equivalent expressions. Material needed: Student pages: Power Up Calculator Lesson Procedure: Warm–Up 10 minutes Prompt: Solar farms are built to collect sunlight and turn it into electricity for homes and businesses. What do you think influences how much energy a solar farm can generate in a day? What would happen to the total energy output if the number of solar panels were doubled? Tripled? Discuss: exponents, rational exponents Guided Instruction 15 minutes Present: scenario for Power Up. Example: Suppose that the performance of a solar battery decreases by a factor of ଵ ଶ every 5 years. If the initial efficiency rating is modeled by the expression 2 ష ఱ , where n is the number of years, what is the efficiency after 3 years? 0.66 Review: key terms – exponent, rules of exponents exponent: the power to which a given number or expression is to be raised rules of exponents: rules followed to simplify expressions involving exponents Independent Practice 20 minutes Distribute: student activity Power Up Allow students to work individually or in pairs. Ask students to look for patterns across problems, such as square roots versus భ మ, and explain why converting between forms can reveal structure or simplify evaluation. Closure 10–15 minutes Review Answers: 1. a. √49; b. 7 2. a. √64 య ; b. 4 hours 3. a. √16 ∙√2ଷ; b. 11.3 4. ଵ ଽ 5. a. 64 units; b. 640 units 6. a. 2ସ; b. 16 Discuss: How do rational exponents help consultants and engineers make better decisions? Can you think of another industry in which understanding rational exponents might also be useful?
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