Lesson Plan: Power and Exponents over the Real Numbers Mathematics

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This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to evaluate real numbers raised to positive and negative integer and zero powers and solve simple exponential equations.

Objectives

Students will be able to

  • recall that a power is a repeated multiplication of the base,
  • evaluate a positive integer power of a real number,
  • evaluate a negative integer power of a real number,
  • evaluate a zero power of a real number,
  • understand the following:
    • if 𝑎∈ℝ−{0} and 𝑛∈ℤ, then 𝑎=1𝑎 and 𝑎=1𝑎,
    • if 𝑎=𝑎 where 𝑎∈ℝ−{−1,0,1}, then 𝑚=𝑛,
    • if 𝑎=𝑏, then 𝑎=𝑏 where 𝑛∈{1,3,5,…} and |𝑎|=|𝑏| where 𝑛∈{2,4,6,…},
  • evaluate algebraic expressions using the rules above,
  • solve exponential equations using the rules above.

Prerequisites

Students should already be familiar with

  • the multiplication of integers, rational numbers, and real numbers,
  • finding positive and negative integer powers of rational numbers,
  • raising rational numbers to the power of zero,
  • the laws of exponents over the rational numbers.

Exclusions

Students will not cover

  • laws of exponents for positive and negative integer powers over the real numbers.

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