Quotient rule for exponents, step by step
Divide two powers of the same base and the exponents subtract.
The question
4⁹ ÷ 4⁹
9−9=0
4⁹ ÷ 4⁹=1
4⁹ ÷ 4⁹=4⁰=1
n=0
- 4⁹ is 9 4s on top and 4⁹ is 9 underneath. Dividing lets them cancel in pairs.
- Every one of them cancels — the same 9 on top and underneath — so what is left is 1.
- The rule says 9 − 9 = 0, so this is 4⁰. Both are right, which is exactly why 4⁰ = 1: it is what the rule has to mean. So n = 0.
How it works.
- 01
4⁹ is 9 4s on top and 4⁹ is 9 underneath. Dividing lets them cancel in pairs.
- 02
Every one of them cancels — the same 9 on top and underneath — so what is left is 1.
- 03
The rule says 9 − 9 = 0, so this is 4⁰. Both are right, which is exactly why 4⁰ = 1: it is what the rule has to mean. So n = 0.