Whole Numbers Divided By Fraction Calculator With Exponents

Equation:

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

Result:

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1. What is This Calculator?

This calculator computes the result of dividing a whole number by a fraction raised to an exponent, using the equivalent multiplication form of the equation.

2. How Does the Calculator Work?

The calculator uses the equation:

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

Where:

\( c \) — Whole number (unitless)
\( a \) — Numerator of fraction (unitless)
\( b \) — Denominator of fraction (unitless)
\( n \) — Exponent (unitless)

3. Mathematical Explanation

Details: Dividing by a fraction is equivalent to multiplying by its reciprocal. When the fraction is raised to an exponent, the exponent applies to both the numerator and denominator.

4. Using the Calculator

Tips: Enter all values as positive numbers. The denominator (b) cannot be zero. The result will be unitless as all inputs are unitless.

5. Frequently Asked Questions (FAQ)

Q1: What if my exponent is negative?
A: Negative exponents are allowed and will invert the fraction before applying the exponent.

Q2: Can I use decimal numbers?
A: Yes, though the calculator is designed for whole numbers, it will accept decimal inputs.

Q3: What happens if I enter zero for a or b?
A: The calculator requires positive values for both numerator and denominator.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places for readability.

Q5: Can this be used for dimensional analysis?
A: No, this calculator is for unitless quantities only.