1. What is the Fraction Power Formula?

The fraction power formula states that a fraction raised to a power equals the numerator raised to that power divided by the denominator raised to that power. This is a fundamental rule in algebra that simplifies calculations with fractional exponents.

2. How Does the Calculator Work?

The calculator demonstrates the mathematical identity:

Where:

• \( a \) — Numerator (any real number)
• \( b \) — Denominator (any non-zero real number)
• \( n \) — Exponent (any real number)

Explanation: The calculator shows both sides of the equation to demonstrate their equality for any valid input values.

3. Mathematical Explanation

Details: This identity comes from the power of a quotient rule in exponents. When you raise a fraction to a power, you can distribute that power to both the numerator and denominator separately.

4. Using the Calculator

Tips: Enter any numbers for numerator and exponent. Denominator must be non-zero. The calculator will show both forms of the calculation to demonstrate their equality.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for negative exponents?
A: Yes, the formula works for all real exponents, including negative ones. A negative exponent means you take the reciprocal of the base.

Q2: What about fractional exponents?
A: The formula also holds true for fractional exponents. For example, (a/b)^(1/2) = √a/√b.

Q3: Why can't the denominator be zero?
A: Division by zero is undefined in mathematics, so the denominator must be a non-zero value.

Q4: Does this work with complex numbers?
A: The basic principle holds, but complex numbers require special consideration with exponents.

Q5: How is this useful in real-world applications?
A: This rule is fundamental in simplifying algebraic expressions, solving equations, and appears frequently in physics and engineering calculations.