Lesson: Power and Exponents over the Real Numbers Mathematics

In this lesson, we will learn how to evaluate real numbers raised to positive and negative integer and zero powers and solve simple exponential equations.

Lesson Plan

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.

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