Multiplying Fractions Calculator 3 Numbers With Exponents

Equation:

\[ (a/b)^k \times (c/d)^l \times (e/f)^m = \frac{a^k \times c^l \times e^m}{b^k \times d^l \times f^m} \]

Numerator 1 (a):

Denominator 1 (b):

Exponent 1 (k):

Numerator 2 (c):

Denominator 2 (d):

Exponent 2 (l):

Numerator 3 (e):

Denominator 3 (f):

Exponent 3 (m):

Result:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is this Calculator?

This calculator computes the product of three fractions raised to different exponents. The formula combines multiplication and exponentiation operations on fractional values.

2. How Does the Calculator Work?

The calculator uses the following equation:

\[ (a/b)^k \times (c/d)^l \times (e/f)^m = \frac{a^k \times c^l \times e^m}{b^k \times d^l \times f^m} \]

Where:

\( a, c, e \) — Numerators of the three fractions
\( b, d, f \) — Denominators of the three fractions
\( k, l, m \) — Exponents for each fraction

3. Mathematical Explanation

Details: The formula combines the rules of exponents and fractions. Each fraction is raised to its respective power, then all are multiplied together. The result simplifies to a single fraction where the numerator is the product of all numerators raised to their powers, and the denominator is the product of all denominators raised to their powers.

4. Using the Calculator

Tips: Enter all numerator, denominator, and exponent values. Default exponents are set to 1. The calculator will return "Undefined" if any denominator is zero.

5. Frequently Asked Questions (FAQ)

Q1: What happens if a denominator is zero?
A: The result will be "Undefined" as division by zero is mathematically undefined.

Q2: Can I use negative exponents?
A: Yes, negative exponents are allowed and will create reciprocal terms in the calculation.

Q3: How precise are the calculations?
A: Results are rounded to 6 decimal places for readability.

Q4: What about fractional exponents?
A: Fractional exponents are supported and will be calculated as roots (e.g., exponent 0.5 = square root).

Q5: Can I use this for more than three fractions?
A: This calculator is designed for three fractions, but the same principle can be extended to more fractions.