1. What is Exponentiation?

Exponentiation is a mathematical operation that involves raising a number (the base) to the power of another number (the exponent). It represents repeated multiplication of the base.

2. How Does the Calculator Work?

The calculator uses the exponentiation formula:

Where:

• \( a \) — The base number
• \( b \) — The exponent (power)

Explanation: When the exponent is a positive integer, exponentiation corresponds to repeated multiplication of the base.

3. Importance of Exponentiation

Details: Exponentiation is fundamental in mathematics, science, engineering, and finance. It's used in compound interest calculations, population growth models, scientific notation, and many other applications.

4. Using the Calculator

Tips: Enter any real number for the base and exponent. The calculator handles both positive and negative numbers, as well as fractional exponents (roots).

5. Frequently Asked Questions (FAQ)

Q1: What happens when the exponent is zero?
A: Any non-zero number raised to the power of 0 equals 1 (a⁰ = 1 where a ≠ 0).

Q2: What about negative exponents?
A: A negative exponent represents the reciprocal of the positive exponent (a⁻ᵇ = 1/aᵇ).

Q3: How are fractional exponents handled?
A: Fractional exponents represent roots (a¹/ᵇ = ᵇ√a).

Q4: What's the result of 0⁰?
A: This is an indeterminate form in mathematics and may be undefined or context-dependent.

Q5: How precise are the calculations?
A: The calculator uses PHP's pow() function which provides floating-point precision.