Fraction to Negative Power Calculator

How to Use This Calculator

Using the fraction to negative power calculator is straightforward:

1. Enter the numerator of your fraction in the first input field.
2. Enter the denominator of your fraction in the second input field.
3. Enter the negative exponent in the third input field (use positive numbers).
4. Click the "Calculate" button to see the result.
5. Review the detailed explanation of the calculation.

The calculator will display the result in its simplest form and provide a step-by-step explanation of how the calculation was performed.

The Formula Explained

When you raise a fraction to a negative power, you're essentially taking the reciprocal of the fraction and then raising it to the positive equivalent of the exponent. The general formula is:

Where:

• a is the numerator of the fraction
• b is the denominator of the fraction
• n is the positive exponent

This formula works because a negative exponent indicates the reciprocal of the base raised to the positive exponent.

Worked Examples

Example 1: Simple Fraction

Calculate (2/3)^-2:

1. First, find the reciprocal: 3/2
2. Then raise to the power: (3/2)² = 9/4

The result is 9/4 or 2.25 in decimal form.

Example 2: Complex Fraction

Calculate (5/8)^-3:

1. Find the reciprocal: 8/5
2. Raise to the power: (8/5)³ = 512/125

The result is 512/125 or 4.096 in decimal form.

Interpreting Results

When you get a result from the fraction to negative power calculator, consider these points:

• The result shows the value of the original fraction raised to the negative power.
• The calculator provides both fractional and decimal forms for better understanding.
• If the result is an improper fraction, it's shown in its simplest form.
• The explanation helps you understand the mathematical steps taken to arrive at the answer.

This interpretation is particularly useful in algebra problems, physics equations, and any context where exponents and fractions are involved.