Walking the ladder down to zero

What is 2⁰? Walk down a ladder of powers, one count each step.

The rule

2⁰ is 1.

Each step down the ladder divides by the base.

Take powers of 2: 16, 8, 4, 2, then 1. These are 2⁴ down to 2⁰. The last step is 2 ÷ 2 = 1.

Any base except 0 ends the same way. The base divided by itself is 1. So any base except 0, to the power 0, is 1.

Subtracting counts agrees. 2³ ÷ 2³ is 2⁰, because 3 − 3 = 0. It is also 8 ÷ 8 = 1.

• 2⁰ = 1
• 10⁰ = 1
• 7⁰ = 1

Try the lab to finish this lesson.