Multiply Three Fractions Calculator 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:

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1. What is Fraction Multiplication with Exponents?

This calculator computes the product of three fractions, each raised to their own exponent. The formula combines the properties of fraction multiplication and exponent rules to simplify complex calculations.

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 fractions
b, d, f — Denominators of the fractions
k, l, m — Exponents for each fraction

3. Mathematical Explanation

Key Concepts:

Fraction multiplication: (a/b) × (c/d) = (a×c)/(b×d)
Exponent rules: (a/b)^n = a^n / b^n
Combining exponents: a^n × a^m = a^(n+m)

4. Using the Calculator

Instructions: Enter all numerators, denominators, and exponents. All denominators must be non-zero. The calculator will compute the combined fraction and the final decimal result.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator requires all denominators to be non-zero.

Q2: Can I use negative exponents?
A: Yes, negative exponents are allowed. They represent reciprocals (x⁻ⁿ = 1/xⁿ).

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

Q4: Can I use this for fractional exponents?
A: Yes, the calculator supports both integer and fractional exponents.

Q5: What's the advantage of this combined form?
A: The combined form often simplifies complex expressions and makes cancellation of terms more apparent.