Fraction Exponent Calculator
Calculate fractions raised to powers and get step-by-step solutions.
How Fraction Exponents Work
When raising a fraction to a power:
\[ \left(\frac{a}{b}\right)^{\frac{m}{n}} = \sqrt[n]{\left(\frac{a}{b}\right)^m} = \frac{\sqrt[n]{a^m}}{\sqrt[n]{b^m}} \]
Properties of Fraction Exponents:
- \[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \]
- \[ \left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n \]
- \[ \left(\frac{a}{b}\right)^{\frac{1}{n}} = \sqrt[n]{\frac{a}{b}} \]
Special Cases:
- When n = 1: \[ \left(\frac{a}{b}\right)^m = \frac{a^m}{b^m} \]
- When m = 1: \[ \left(\frac{a}{b}\right)^{\frac{1}{n}} = \sqrt[n]{\frac{a}{b}} \]
- When m = n: \[ \left(\frac{a}{b}\right)^{\frac{n}{n}} = \frac{a}{b} \]
Applications:
- Scientific calculations
- Engineering computations
- Financial mathematics
- Physics and chemistry