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).

Base (x)
Any real number (negative allowed with odd denominator).
Numerator (n)
Enter a whole number (can be negative).
Denominator (d)
Enter a whole number greater than 0.
Results
Fractional exponent (a)
Computed as a = x^(n/d).
x^(n/d) = ?
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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.

Rational exponent notation =
x^(n/d) = (d√x)^n

Take the d-th root first, then raise to n.

Equivalent form =
x^(n/d) = d√(x^n)

Raise to n first, then take the d-th root.

Special case =
x^(1/d) = d√x

An exponent of 1/d is a root.

x
= Base value
n
= Numerator (power)
d
= Denominator (root index)
d√x
= The d-th root of x
Calculate fractional exponent example
27^(2/3) = (3√27)^2 = 3^2 = 9

Cube root of 27 is 3, then square it.

Another example
16^(3/4) = (4√16)^3 = 2^3 = 8

Fourth root of 16 is 2, then cube it.

How to Use the Fractional Exponent Calculator

  1. 1

    Enter the base value x.

  2. 2

    Enter the numerator n (the power).

  3. 3

    Enter the denominator d (the root index).

  4. 4

    The calculator returns x^(n/d), using the fractional exponents formula.

Frequently Asked Questions

How do you calculate fractional exponent?

Use x^(n/d) = (d√x)^n. Take the d-th root of x, then raise to n.

What is the fractional exponents formula?

x^(n/d) = (d√x)^n = d√(x^n).

What is rational exponent notation?

It’s writing roots as exponents, like x^(1/2) for √x or x^(1/3) for ∛x.

Is this a fractional exponent solver?

Yes—it evaluates expressions of the form x^(n/d) and shows the equivalent root-and-power interpretation.

Can I use this as a rational exponent equations calculator?

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.

What about negative bases?

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.