1. What is Power Calculation?

The power operation (a^b) represents the base (a) multiplied by itself exponent (b) times. It's a fundamental mathematical operation used in various fields including physics, engineering, and finance.

2. How Does the Calculator Work?

The calculator uses the power function:

Where:

• \( a \) — Base value (any real number)
• \( b \) — Exponent value (any real number)

Explanation: The calculator computes the result of raising the base to the power of the exponent.

3. Mathematical Explanation

Details: For positive integer exponents, a^b means a multiplied by itself b times. For fractional exponents, it represents roots (a^(1/b) is the b-th root of a). Negative exponents represent reciprocals (a^-b = 1/(a^b)).

4. Using the Calculator

Tips: Enter any real numbers for base and exponent. The calculator will compute the result with precision to 4 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: What happens when the exponent is 0?
A: Any non-zero number raised to the power of 0 equals 1 (a^0 = 1 where a ≠ 0). 0^0 is undefined.

Q2: How are negative exponents handled?
A: A negative exponent means taking the reciprocal of the positive power (a^-b = 1/(a^b)).

Q3: What about fractional exponents?
A: Fractional exponents represent roots (a^(1/b) is the b-th root of a, a^(c/b) is the b-th root of a raised to power c).

Q4: What's the largest/smallest number I can calculate?
A: The calculator uses PHP's pow() function which handles numbers within approximately ±1.8e308 with about 14-15 digits precision.

Q5: How are imaginary numbers handled?
A: This calculator returns "NAN" for results involving imaginary numbers (like square roots of negative numbers with even denominators).