Learning Goal
Explain rational exponents
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
**HSN.RN.A.1**: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))³ = 5^((1/3)·3) to hold, so (5^(1/3))³ must equal 5.
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HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))³ = 5^((1/3)·3) to hold, so (5^(1/3))³ must equal 5.
What you'll learn
- Explain why 5^(1/3) must equal the cube root of 5, using the reasoning that (5^(1/3))³ must equal 5^((1/3)·3) = 5¹ = 5
- Extend integer exponent properties (product rule, power rule, quotient rule) to rational exponents and justify each extension
- Interpret rational exponents as radicals: a^(1/n) = ⁿ√a and a^(m/n) = (ⁿ√a)^m = ⁿ√(a^m)
- Evaluate expressions with rational exponents by converting between exponential and radical notation
- Explain in their own words why the definition of rational exponents is not arbitrary but is forced by the requirement that exponent properties remain consistent
Slides
Step through the lesson, or watch it as a narrated video • 2 slide decks
Explain rational exponents part 1
✓ Start hereExplain rational exponents part 2
Practice
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