Raise fractions to any power and get simplified results. Compute $(a/b)^n$ instantly with automatic GCD reduction and decimal conversion.
Last updated: May 2026 | By Patchworkr Team
| Expression | Result | Notes |
|---|---|---|
| (2/3)^2 | 4/9 | Square both numerator and denominator |
| (3/2)^-1 | 2/3 | Negative exponent flips the fraction |
| (1/2)^3 | 1/8 | Power of a unit fraction |
| (4/9)^(1/2) | ≈ 0.6667 | Fractional exponent → root (decimal result) |
Raising a fraction to a power means multiplying the fraction by itself a specified number of times: (a/b)^n = (a/b) × (a/b) × ... × (a/b) n times. Mathematically, this equals a^n / b^n—raise both numerator and denominator to the same power independently. For example, (2/3)^3 = 2^3 / 3^3 = 8/27. Fraction exponents are fundamental to algebra, calculus, physics, and engineering, appearing in formulas for compound interest, decay models, geometric scaling, and quantum mechanics. Understanding this operation bridges arithmetic with more advanced mathematics.
Fraction exponents possess important properties: (a/b)^0 = 1 for any non-zero fraction, (a/b)^1 = a/b, and negative exponents create reciprocals: (a/b)^(-n) = (b/a)^n. When exponents are fractions themselves (like (a/b)^(1/2)), they represent roots: fractional exponents unify power and root operations under one framework. This calculator automatically simplifies results using GCD reduction, presenting answers in the most useful form—either as a simplified fraction or as a decimal when appropriate.
Input the top number (numerator) and bottom number (denominator) of your fraction. For example, for 2/3, enter 2 and 3 respectively.
Type the exponent n in the third field. This is the power to which the fraction will be raised. Use positive integers, negative integers, or decimals.
The calculator raises the fraction to the specified power using the rule (a/b)^n = a^n / b^n. Integer exponents produce exact fraction results.
The calculator reduces the result to simplest form by dividing numerator and denominator by their GCD. If applicable, decimal equivalents are shown.
Cross-check by computing a^n and b^n separately, then forming the fraction a^n/b^n. For (2/3)^2: numerator = 2^2 = 4, denominator = 3^2 = 9, result = 4/9.
What is (2/3) raised to the power 3?
It means multiply the fraction a/b by itself n times: (a/b)^n = (a/b) × (a/b) × ... × (a/b). This equals a^n / b^n by the power rule for fractions.
Negative exponents create reciprocals: (a/b)^(-n) = (b/a)^n. For example, (2/3)^(-2) = (3/2)^2 = 9/4. The fraction is flipped and the exponent becomes positive.
Any non-zero number raised to the power 0 equals 1. So (a/b)^0 = 1 for any fraction a/b where a ≠ 0. This is a fundamental law of exponents.
Fractional exponents represent roots: (a/b)^(1/2) is the square root of a/b. This calculator handles integer and decimal exponents; fractional exponents produce decimal results.
Simplified form (lowest terms) is the standard mathematical convention. By dividing numerator and denominator by their GCD, the result is easier to understand, compare, and use in further calculations.
Yes, but results may become extremely large or small. For example, (2/3)^10 produces very large numerators and denominators. The calculator handles these computations accurately within numerical precision limits.
These are different! (a/b)^n = a^n/b^n (exponent applies to entire fraction), while a/(b^n) only raises the denominator. For (2/3)^2 = 4/9, but 2/(3^2) = 2/9. Order of operations matters.
Raise numerator and denominator separately to the power: (a/b)^n means compute a^n and b^n separately, then form a^n/b^n. Finally, simplify by dividing by the GCD. Manual calculation demonstrates the underlying mathematics.
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