How do you raise a fraction to a power?
Raise the numerator and denominator to that power, then simplify.
Fraction Exponent Calculator
Compute (a/b)^n for an integer exponent and see the simplified fraction and decimal.
Enter a fraction and exponent
Provide numerator, denominator, and an integer power n.
About this calculator
How to use Fraction Exponent Calculator, plus the formulas and logic behind the results.
Tool description
Raising a fraction to an integer power multiplies the fraction by itself n times, or takes the reciprocal for negative exponents.
How to use
- Enter the base fraction a/b.
- Enter an integer exponent between −10 and 10.
- Select Calculate to view (a/b)^n.
- Review the simplified result and decimal.
Formulas & reference
(a/b)^n = a^n / b^n for n ≥ 0(a/b)^(−n) = (b/a)^n when a ≠ 0(a/b)^0 = 1 for a/b ≠ 0
Power tips
- (2/3)^2 = 4/9
- (1/2)^3 = 1/8
- (2/5)^(−1) = 5/2
- Any non-zero fraction to the 0 is 1
Calculation logic
Positive exponents power numerator and denominator separately. Negative exponents invert first, then power. Zero exponent returns 1 for non-zero bases.
Exponents are limited to keep integer powers within a practical range. Zero to a non-positive power is rejected.
Fraction Exponent Calculator FAQ
Common questions about this calculator and how to use the results.
What does a negative exponent mean?
A negative exponent means take the reciprocal, then raise to the positive power.
What is (a/b)^0?
Any non-zero fraction raised to the power 0 equals 1.
Why is the exponent limited?
Limits keep results from becoming extremely large or tiny for display.
Can the base be negative?
Yes. Odd powers preserve the negative sign; even powers make it positive.
Is the result simplified?
Yes. The powered fraction is reduced to lowest terms.