1. What is Fraction Multiplication with Exponents?

This calculator computes the product of two fractions raised to different exponents using the mathematical identity: \[ (a/b)^m \times (c/d)^n = (a^m c^n)/(b^m d^n) \] It simplifies complex fraction multiplication problems with exponents.

2. How Does the Calculator Work?

The calculator applies the following steps:

1. Raises numerator a to the power of m
2. Raises denominator b to the power of m
3. Raises numerator c to the power of n
4. Raises denominator d to the power of n
5. Multiplies the powered numerators together
6. Multiplies the powered denominators together
7. Divides the final numerator by the final denominator

3. Mathematical Explanation

The formula works because of exponent rules:

• \((a/b)^m = a^m/b^m\) (Power of a quotient rule)
• \(a^m \times c^n = a^m c^n\) (Multiplication of terms with exponents)
• \(b^m \times d^n = b^m d^n\) (Same as above for denominators)

Key Properties: The exponents must be applied before multiplication, and denominators cannot be zero.

4. Using the Calculator

Instructions: Enter all six values (two numerators, two denominators, two exponents). All fields are required. Denominators cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: Can I use negative exponents?
A: Yes, negative exponents are allowed. They represent reciprocals (e.g., a⁻ⁿ = 1/aⁿ).

Q2: What about fractional exponents?
A: Fractional exponents are supported (e.g., 0.5 represents square root).

Q3: Why do I get an error when denominators are zero?
A: Division by zero is mathematically undefined, so the calculator requires non-zero denominators.

Q4: Can I chain more than two fractions?
A: This calculator handles two fractions, but the principle extends to any number of fractions.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places for readability while maintaining reasonable precision.