Everyone is coming up with these more elaborate explanations because they’re starting with the premise that 2^3 is best interpreted as “multiply 3 twos together”.
A description of exponentiation (by integer powers is) that naturally extends to zero is, “Start with 1. Multiply it by the number on the bottom, repeating that process by the number on the top times”. So:
2^4 = 1 × 2 × 2 × 2 × 2 (Multiply 1 by 2 four times.)
2^3 = 1 × 2 × 2 × 2 (Multiply 1 by 2 three times.)
2^2 = 1 × 2 × 2 (Multiply 1 by 2 two times.)
2^1 = 1 × 2 (Multiply 1 by 2 once.)
2^0 = 1 (Multiply 1 by 2 zero times.)
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