Fractional Exponent Calculator

Work out fractional exponent instantly with clear inputs, formula shown and shareable results.

About Fractional Exponent Calculator

A fractional exponent combines a root and a power: b^(p/q) is the qth root of b raised to the p, and it makes no difference which you do first.

Formula

Fractional exponent

b^(p/q) = (ᵍ√b)ᵖ = ᵍ√(bᵖ)

Worked example

With the default values below, Fractional Exponent Calculator returns b^(p/q) of 4.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Base bminimum 0: 8
Exponent numerator p: 2
Exponent denominator qminimum 0: 3

Results

b^(p/q): 4.00000000
The qth root of b: 2.00000000
Taking the root first, then the power: 4.00000000
Exponent as a decimal: 0.66666667

Step by step

1Values used
2Fractional exponent
3b^(p/q)= 4.00000000
4The qth root of b= 2.00000000
5Taking the root first, then the power= 4.00000000
6Exponent as a decimal= 0.66666667

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is 8^(2/3)?

The cube root of 8 is 2, and 2² = 4.

Why avoid negative bases?

Because (−8)^(1/2) has no real value, and even (−8)^(1/3) is handled inconsistently by different conventions.