A learner sees 5⁰ = 1 and objects that “anything times zero is zero.” The objection reveals a useful misunderstanding: the small raised zero is an exponent, not an instruction to multiply the base by zero.
Begin with a pattern the learner already understands. Write 5³ = 125, 5² = 25 and 5¹ = 5 in a column. Ask what happens to the result each time the exponent decreases by one.
Continue the division pattern
Each step divides by five. Continuing one more step gives 5⁰ = 1. Repeat with a different nonzero base, such as two: 8, 4, 2, 1. The result is not an isolated rule attached to the number five.
Now compare 5 × 0 with 5⁰. Say each expression aloud and ask the learner to describe the operation. Keeping the two notations side by side can make the source of the confusion visible.
Explain the condition
For a nonzero number a, the quotient aⁿ divided by aⁿ equals one. Applying the exponent rule gives aⁿ⁻ⁿ, or a⁰. This connects the result to a rule the learner may already use.
The nonzero condition matters because this reasoning divides by a power of the base. Do not use it to settle 0⁰. That expression needs its own context and is not established by an argument that would require division by zero.
For a quick check, ask the learner to explain 7⁰ without quoting the rule alone, then identify why 7 × 0 is different. Let them draw the descending pattern if that is clearer than symbolic algebra.
A successful explanation gives the learner a route back to the result. They can reconstruct why the answer is one instead of remembering a surprising exception with no connection to the rest of arithmetic.