1. What is a Fraction with Negative and Exponent?

This calculator computes the value of a negative fraction raised to an exponent. The general form is (-a/b)^exp, where 'a' is the numerator, 'b' is the denominator, and 'exp' is the exponent.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( a \) — Numerator (can be positive or negative)
• \( b \) — Denominator (must be positive)
• \( exp \) — Exponent (can be positive, negative, or fractional)

Explanation: The calculator first creates the negative fraction, then raises it to the specified power using exponentiation rules.

3. Importance of Fraction Calculations

Details: Calculating fractions with exponents is fundamental in algebra, physics, engineering, and financial mathematics. Understanding negative exponents is particularly important for inverse relationships.

4. Using the Calculator

Tips: Enter the numerator (can be positive or negative), denominator (must be positive), and exponent (can be any real number). The denominator cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What happens with negative exponents?
A: A negative exponent means taking the reciprocal of the base raised to the positive exponent. For example, (-1/2)^-3 = (-2)^3 = -8.

Q2: Can the denominator be negative?
A: The calculator automatically handles the negative sign in the numerator, so denominator should be positive for clarity.

Q3: What about fractional exponents?
A: Fractional exponents are supported. For example, (-1/4)^(1/2) would calculate the square root of -0.25 (which is a complex number).

Q4: How are odd/even exponents handled?
A: Odd exponents preserve the sign, even exponents make the result positive. For example, (-1/3)^3 remains negative, while (-1/3)^2 becomes positive.

Q5: What's the precision of the calculator?
A: Results are calculated with floating-point precision and rounded to 4 decimal places for display.