🔢 Fraction Exponent Calculator
Calculate base raised to fractional exponent
Fraction Exponent (numerator/denominator)
Exponent: numerator/denominator (e.g., 2/3 means cube root of base squared)
How to Use This Calculator
Enter Base
Input the base number that will be raised to a fractional power.
Enter Fraction Exponent
Input the numerator and denominator of the fractional exponent (e.g., 2/3 means cube root of base squared).
Calculate
Press "Calculate" to find base^(numerator/denominator).
Formula
base^(numerator/denominator) = (denominator√base)^numerator
or: base^(numerator/denominator) = denominator√(base^numerator)
Example: 8^(2/3)
8^(2/3) = (³√8)² = 2² = 4
Or: 8^(2/3) = ³√(8²) = ³√64 = 4
The fraction exponent means: raise base to numerator power, then take denominator root
About Fraction Exponent Calculator
The Fraction Exponent Calculator calculates base raised to a fractional exponent (rational power). A fractional exponent m/n means: raise base to m power, then take the nth root (or take nth root first, then raise to m power).
When to Use This Calculator
- Algebra: Calculate fractional powers
- Mathematics: Work with rational exponents
- Education: Learn fractional exponents
- Science: Calculate fractional powers in formulas
Understanding Fraction Exponents
A fraction exponent m/n means: base^(m/n) = (n√base)^m = n√(base^m). The denominator is the root (e.g., 3 means cube root), and the numerator is the power (e.g., 2 means square).
Frequently Asked Questions
What is a fraction exponent?
A fraction exponent is a rational number (m/n) used as an exponent. It means: raise base to m power, then take the nth root. For example, 8^(2/3) = (³√8)² = 2² = 4.
How do I calculate base^(m/n)?
Two ways: (1) Take nth root first, then raise to m: base^(m/n) = (n√base)^m. (2) Raise to m first, then take nth root: base^(m/n) = n√(base^m). Both give the same result.
Can I use negative bases?
Yes, but only if the root is odd (odd denominator). Even roots of negative numbers are not real (they're complex). For example, (-8)^(1/3) = -2, but (-8)^(1/2) is not real.
What if the fraction is simplified?
The calculator automatically simplifies the fraction exponent. For example, 2/4 = 1/2, 4/6 = 2/3, etc. The simplified form is used for the calculation.