M4.1.2 For the adult
Zero and negative powers
You cannot multiply by 5 no times, so what can 5⁰ mean?
What this chapter teaches
Each step down the powers of a number divides by that number. That pattern reaches a⁰ = 1 and carries on to 2⁻³ = 1/8. A negative index means one over the positive power, and never a negative number.
Three questions to ask
There is no one right wording. Listen for the idea.
- What happens to 2³, 2², 2¹ as the index goes down, and what comes next?
- Why is 5⁰ equal to 1 and not 0?
- How would you write 10⁻² as a fraction and as a decimal?
After the chapter, the learner can
- Explain why 5⁰ = 1
- Write 2⁻³ as 1/8
What they copy into their notebook
a⁰ = 1 for any a except 0. A negative index means one over: 2⁻³ = 1/2³ = 1/8. Going down the ladder divides each time. The answer stays above 0.