Fraction Exponent Calculator
Calculate powers with fractional and negative exponents with step-by-step solutions
Calculate Fractional Exponents
The number to be raised to a power
Top part of the fraction
Bottom part of the fraction (cannot be 0)
Expression
Result
Special Cases:
Step-by-Step Solution
Common Fractional Exponents
Root Exponents (n = 1)
Mixed Exponents
Exponent Rules
Fractional Exponent
xn/d = (ᵈ√x)n = ᵈ√(xn)
Negative Exponent
x-n = 1/xn
Root Form
x1/n = ⁿ√x
Power of Product
(xy)n = xnyn
Calculator Tips
Enter negative numbers for negative exponents
Base can be fractions (e.g., 0.5 for ½)
Denominator = 1 for integer exponents
Even roots of negative numbers are undefined
Result shows exact form when possible
Understanding Fractional Exponents
What Are Fractional Exponents?
Fractional exponents are a way of expressing both powers and roots in one notation. They combine the concepts of exponentiation and root extraction into a unified mathematical expression.
Basic Forms
- •x1/n: The n-th root of x
- •xm/n: The n-th root of x raised to the m-th power
- •x-m/n: The reciprocal of xm/n
Calculation Methods
Method 1: Root First
xm/n = (ⁿ√x)m
Take the n-th root, then raise to power m
Method 2: Power First
xm/n = ⁿ√(xm)
Raise to power m, then take the n-th root
Negative Exponents
x-m/n = 1/(xm/n)
Take the reciprocal of the positive exponent
Common Applications
Physics & Engineering
Power laws, scaling relationships, dimensional analysis
Finance & Economics
Compound interest, growth models, elasticity calculations
Computer Science
Algorithm complexity, fractional algorithms, optimization
Important Properties
Domain Restrictions
- • Even roots of negative numbers are undefined (in real numbers)
- • Zero raised to negative powers is undefined
- • Division by zero in denominators is undefined
Calculation Tips
- • Choose the method that gives simpler intermediate values
- • Simplify the fraction exponent first when possible
- • Use calculator for non-perfect powers and roots