Multiplying With Fractions Calculator With Exponents

Fraction Multiplication with Exponents Formula:

\[ \left(\frac{a}{b}\right)^n \times \left(\frac{c}{d}\right)^m = \frac{a^n \times c^m}{b^n \times d^m} \]

Numerator 1 (a):

Denominator 1 (b):

Exponent 1 (n):

Numerator 2 (c):

Denominator 2 (d):

Exponent 2 (m):

Calculation Result:

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1. What is Fraction Multiplication with Exponents?

This calculator computes the product of two fractions each raised to their own exponents. The formula combines the rules of fraction multiplication with the laws of exponents to simplify complex calculations.

2. How Does the Calculator Work?

The calculator uses the following mathematical formula:

\[ \left(\frac{a}{b}\right)^n \times \left(\frac{c}{d}\right)^m = \frac{a^n \times c^m}{b^n \times d^m} \]

Where:

\( a \) — First numerator
\( b \) — First denominator
\( n \) — First exponent
\( c \) — Second numerator
\( d \) — Second denominator
\( m \) — Second exponent

Explanation: The formula shows that when multiplying two fractions with exponents, you can multiply the numerators (each raised to their exponent) and denominators (each raised to their exponent) separately.

3. Importance of Fraction Exponents

Details: Understanding how exponents work with fractions is crucial in algebra, physics, engineering, and many scientific calculations where ratios are raised to powers.

4. Using the Calculator

Tips: Enter all numerator, denominator, and exponent values. Denominators cannot be zero. The calculator will show the step-by-step calculation along with the final result.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominator is zero?
A: Division by zero is undefined. The calculator requires non-zero denominators.

Q2: Can I use negative exponents?
A: Yes, negative exponents are allowed and will be calculated correctly.

Q3: How precise are the calculations?
A: Calculations are performed with floating-point precision and displayed to 6 decimal places.

Q4: Can I use fractional exponents?
A: Yes, the calculator supports fractional exponents (like 0.5 for square roots).

Q5: What's the difference between (a/b)^n and a^n/b^n?
A: Mathematically they are equivalent - this is one of the laws of exponents.