1. What Is This Fraction Calculation?

This calculator computes the result of a fractional expression with exponents and multiplication: (a/b)^n × (c/d). It demonstrates how exponents distribute across fractions and how to multiply fractions together.

2. How The Formula Works

The calculator uses the mathematical identity:

Where:

• \( a \) — First numerator (unitless)
• \( b \) — First denominator (unitless)
• \( n \) — Exponent (unitless)
• \( c \) — Second numerator (unitless)
• \( d \) — Second denominator (unitless)

3. Mathematical Explanation

Step-by-step:

1. Apply exponent to the first fraction: (a/b)^n = a^n / b^n
2. Multiply by the second fraction: (a^n / b^n) × (c/d)
3. Multiply numerators: a^n × c
4. Multiply denominators: b^n × d
5. Combine into single fraction: (a^n × c)/(b^n × d)

4. Using The Calculator

Instructions: Enter values for all five parameters (a, b, n, c, d). Denominators (b and d) cannot be zero. The calculator will show both the final result and the step-by-step calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why does the exponent apply to both numerator and denominator?
A: This is the power of a quotient rule in exponents: (a/b)^n = a^n / b^n.

Q2: What if I have negative exponents?
A: The calculator handles negative exponents correctly, as they represent reciprocals (x^-n = 1/x^n).

Q3: Can I use decimal values for the exponent?
A: Yes, the calculator accepts any real number for the exponent, including fractions and decimals.

Q4: What happens if I enter zero for a denominator?
A: The calculator will not compute a result as division by zero is undefined in mathematics.

Q5: How precise are the calculations?
A: Results are calculated with floating-point precision and rounded to 4 decimal places for display.