Dividing powers with the same base subtracts exponents: 10⁸ ÷ 10⁵ = 10³. It explains why a⁰ = 1 (aⁿ/aⁿ) and why negative exponents are reciprocals.
How to use the Dividing Exponents Calculator
- Operation
- Base a
- Exponent m
- Base b
- Exponent n
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter both powers. Same bases subtract exponents; same exponents divide the bases; otherwise each power is evaluated.
Formula
aᵐ ÷ aⁿ = a^(m − n), aⁿ ÷ bⁿ = (a/b)ⁿ
Worked example
Inputs — Operation: Divide aᵐ ÷ bⁿ; Base a: 5; Exponent m: 7; Base b: 5; Exponent n: 4.
Results — Simplified = 5³; Value = 125; Rule = Same base: subtract the exponents: 7 − 4 = 3; Each power = 5⁷ = 78,125
5⁴ = 625.
Key terms
- Quotient of powers
- aᵐ/aⁿ = aᵐ⁻ⁿ.
Frequently asked questions
What is x⁷ ÷ x⁴?
x³.
Why is a⁰ = 1?
aⁿ ÷ aⁿ = a⁰, and any non-zero number divided by itself is 1.
What is 6⁴ ÷ 3⁴?
2⁴ = 16.
What if the result exponent is negative?
It means a reciprocal: 2³ ÷ 2⁵ = 2⁻² = 1/4.