Fractional Exponent Calculator
Use our fractional exponent calculator to calculate fractional exponent values like x^(n/d). Includes the fractional exponents formula, rational exponent notation, and help for solving rational exponent equations (fractional exponent solver).
What is a Fractional Exponent?
A fractional exponent (also called a rational exponent) is an exponent written as a fraction, like n/d. It combines powers and roots in one expression.
In rational exponent notation, x^(n/d) means “take the d-th root of x, then raise it to the power n” (or equivalently raise x to n, then take the d-th root).
This fractional exponent calculator helps you calculate fractional exponent expressions quickly and supports common rational exponent equations calculator use cases.
Fractional Exponents Formula
Fractional exponents rewrite powers as roots. These rules are the core of fractional exponent solver steps and rational exponent notation.
Take the d-th root first, then raise to n.
Raise to n first, then take the d-th root.
An exponent of 1/d is a root.
Cube root of 27 is 3, then square it.
Fourth root of 16 is 2, then cube it.
How to Use the Fractional Exponent Calculator
- 1
Enter the base value x.
- 2
Enter the numerator n (the power).
- 3
Enter the denominator d (the root index).
- 4
The calculator returns x^(n/d), using the fractional exponents formula.
Frequently Asked Questions
Use x^(n/d) = (d√x)^n. Take the d-th root of x, then raise to n.
x^(n/d) = (d√x)^n = d√(x^n).
It’s writing roots as exponents, like x^(1/2) for √x or x^(1/3) for ∛x.
Yes—it evaluates expressions of the form x^(n/d) and shows the equivalent root-and-power interpretation.
For evaluating a single expression x^(n/d), yes. For full equations (solving for x), you’d usually rearrange using exponent rules and then compute.
Some fractional exponents can produce non-real results. For odd denominators (like 1/3), negative bases can still be real (∛(-8) = -2). For even denominators (like 1/2), negative bases are not real in the real-number system.