1. What is the Power of Fractions?

The power of a fraction follows the same rules as exponentiation of whole numbers. When a fraction is raised to a power, both the numerator and denominator are raised to that power.

2. How Does the Calculator Work?

The calculator uses the fraction power formula:

Where:

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

Explanation: The formula shows that raising a fraction to a power is equivalent to raising both the numerator and denominator to that power separately.

3. Mathematical Explanation

Details: This property comes from the rules of exponents. When multiplying fractions, we multiply numerators and denominators separately. Raising to a power is repeated multiplication, so the exponent applies to both parts of the fraction.

4. Using the Calculator

Tips: Enter the numerator, denominator (must be non-zero), and exponent. The calculator will show the result of the fraction raised to the power, as well as the separate numerator and denominator powers.

5. Frequently Asked Questions (FAQ)

Q1: Can the denominator be zero?
A: No, division by zero is undefined in mathematics. The denominator must be a non-zero value.

Q2: What about negative exponents?
A: Negative exponents represent reciprocals. The formula works for any real exponent, positive or negative.

Q3: Can this be used with complex numbers?
A: This calculator handles real numbers only. Complex number exponentiation follows different rules.

Q4: What if the exponent is a fraction?
A: Fractional exponents represent roots. The formula works the same way (e.g., (a/b)^(1/2) = √a/√b).

Q5: Why is this property useful?
A: It simplifies calculations by allowing you to work with numerator and denominator separately, especially helpful in algebraic manipulations.