Dividing Exponents Calculator
Apply the exponent quotient rule: when you divide two powers with the same base, subtract the exponents. Enter the base, the exponent of the numerator and the exponent of the denominator to get the result and a worked step-by-step solution.
3^5 ÷ 3^2 = 3^3
- 1
Subtract exponents
5 − 2 = 3 - 2
Apply quotient rule
3^3a^m ÷ a^n = a^(m−n) — bases are equal so subtract exponents. - 3
Result
3^3 = 27
How does this calculator work?
a^m ÷ a^n = a^(m−n): just subtract exponents when the base is the same. For example, 3^5 ÷ 3^2 = 3^3 = 27. If m < n the result exponent is negative, giving a fraction. Enter the base, m and n to get the numerical result and a step-by-step breakdown.
Formula
How this is calculated
The quotient rule for exponents states that dividing two powers with the same base is equivalent to keeping the base and subtracting the exponents: a^m ÷ a^n = a^(m−n). This works because each factor of a in the denominator cancels one factor of a in the numerator.
For example, 3^5 ÷ 3^2 = 3^(5−2) = 3^3 = 27. The rule holds for any real base (except 0 in cases that produce 0^0 or negative exponents of 0) and any real exponents, including negative and fractional ones. A negative result exponent produces a fraction: a^(−k) = 1/a^k.
This calculator evaluates both individual powers and the final result numerically. For very large bases or exponents, floating-point overflow may occur (JavaScript's maximum safe float is about 1.8×10^308). The step-by-step display makes the application of the rule explicit.
Frequently asked questions
Because a^m = a × a × … (m times) and a^n = a × a × … (n times). Dividing cancels n copies of a from the numerator, leaving a^(m−n) copies.
If m = n, then a^m ÷ a^n = a^0 = 1 (for any non-zero base). This is the definition of the zero exponent.
Yes. a^(1/2) ÷ a^(1/4) = a^(1/2 − 1/4) = a^(1/4). And a^2 ÷ a^5 = a^(2−5) = a^(−3) = 1/a^3. The rule is general for all real exponents.
Also known as
TG we-Calculate Editorial Team. (2026). Dividing Exponents Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/dividing-exponents-calculator
TG we-Calculate Editorial Team. "Dividing Exponents Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/dividing-exponents-calculator.
TG we-Calculate Editorial Team, "Dividing Exponents Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/dividing-exponents-calculator
@misc{wecalculate_dividing_exponents_calculator, title = {Dividing Exponents Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/dividing-exponents-calculator}}, year = {2026}, note = {TG we-Calculate} }
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