Lesson Plan: Laws of Exponents over the Real Numbers Mathematics • 9th Grade

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to apply the laws of exponents to multiply and divide powers and to calculate a power raised to a power over the real numbers.

Objectives

Students will be able to

  • understand and use the laws of exponents over the Real numbers:
    • if π‘Žβˆˆβ„ and π‘š,π‘›βˆˆβ„€, then π‘ŽΓ—π‘Ž=π‘Žο‰οŠο‰οŠ°οŠ,
    • if π‘Žβˆˆβ„ and π‘š,π‘›βˆˆβ„€βˆ’[0] where π‘šβ‰₯𝑛, then π‘ŽΓ·π‘Ž=π‘Žο‰οŠο‰οŠ±οŠ,
    • if π‘Ž,π‘βˆˆβ„ and π‘›βˆˆβ„€, then (π‘Žπ‘)=π‘ŽΓ—π‘οŠοŠοŠ,
    • if π‘Ž,π‘βˆˆβ„βˆ’[0] and π‘›βˆˆβ„€, then ο€»π‘Žπ‘ο‡=π‘Žπ‘οŠοŠοŠ,
    • if π‘Žβˆˆβ„ and π‘š,π‘›βˆˆβ„€, then (π‘Ž)=π‘Žο‰οŠο‰οŠ,
  • apply the laws of exponents to expressions with more than two terms,
  • use the laws of exponents to simplify exponential expressions involving real numbers,
  • use the laws of exponents to evaluate algebraic expressions,
  • solve exponential equations using the rules above.

Prerequisites

Students should already be familiar with

  • evaluating positive and negative integer powers of real numbers,
  • evaluating zero powers of real numbers,
  • the laws of exponents over the rational numbers.

Exclusions

Students will not cover

  • operations on powers.

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