This all-in-one online Fraction Exponent Calculator is designed to find the fractional exponent of a number x of the form xn/d, where the base x, the numerator n and the denominator d are real numbers. You can enter the values of any three parameters in the input fields of this calculator and find the missing parameter.
Fractional Exponents
Exponent, or power, is a way of indicating that a quantity x is to be multiplied by itself some number of times. In the expression xn, x is called the base and n is called the exponent, or power. In general,
where x is multiplied by itself n times.
A base may also be raised to a negative, fractional, or decimal power.
The following identity for negative exponents holds for any integer n and nonzero x:
The exponent of the form x1/n is defined as the principal n-th root of a positive real number x, because we have the following equality:
So, we come to the formulation of the exponent with rational power:
Exponentiation to real powers of positive real numbers can be defined either by extending the rational powers to reals by continuity, or more usually as given in powers via logarithms. The result is always a positive real number, and the identities and properties shown for integer exponents are true for positive real bases with non-integer exponents as well.
Related calculators
Check out our other math calculators such as Simplifying Radical Expressions Calculator or Prime Factorization Calculator.