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:

• \( a \) — Base (unitless)
• \( b \) — Exponent (unitless)

Explanation: The base is multiplied by itself as many times as indicated by the exponent value.

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 the base and exponent values. Both values are unitless. The calculator supports both integer and decimal exponents.

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. Zero raised to the power of 0 is undefined.

Q2: How are negative exponents handled?
A: A negative exponent represents the reciprocal of the base raised to the positive exponent (a⁻ᵇ = 1/aᵇ).

Q3: What about fractional exponents?
A: Fractional exponents represent roots (a¹/ⁿ = ⁿ√a). The calculator handles decimal exponents accurately.

Q4: Are there any limitations to this calculator?
A: The calculator uses standard PHP mathematical functions and may have precision limitations with very large or very small numbers.

Q5: Can I calculate complex numbers with this calculator?
A: No, this calculator only handles real numbers for both base and exponent inputs.