Fractions with Exponents Calculator
Calculate fractions raised to positive, negative, or fractional powers. Includes tooltips explaining the exponent rules and step-by-step simplification.
About
Exponents add a layer of complexity to fractions that often confuses students, particularly when negative signs or decimals are involved. Understanding that a negative exponent 'flips' the fraction, or that a fractional exponent represents a root, is key to mastering algebra.
This tool is designed to isolate and solve these specific problems. It is extensively used by students in Algebra 2 and Pre-Calculus to verify manual calculations of power rules. It ensures that the order of operations (PEMDAS) is respected and clearly illustrates how the power distributes to both the numerator and the denominator.
Formulas
The two most critical laws applied here are the distribution of powers and the reciprocal rule for negative indices.
When the exponent is a fraction (e.g., 1/2), it translates to a radical:
Reference Data
| Rule Name | Formula | Example (x=2, y=3) |
|---|---|---|
| Power of a Quotient | (a/b)^n = a^n / b^n | (2/3)^2 = 4/9 |
| Negative Exponent | (a/b)^-n = (b/a)^n | (2/3)^-2 = (3/2)^2 = 9/4 |
| Zero Exponent | (a/b)^0 = 1 | (99/100)^0 = 1 |
| Fractional Exponent | (a/b)^(1/n) = n√(a/b) | (4/9)^(1/2) = 2/3 |
| Product of Powers | (a/b)^n * (a/b)^m | Add exponents: n+m |
| Quotient of Powers | (a/b)^n / (a/b)^m | Subtract exponents: n-m |
| Power of a Power | ((a/b)^n)^m | Multiply exponents: n*m |