1. What is Exponentiation?

Exponentiation is a mathematical operation that raises 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:

• \( base \) — The number being multiplied
• \( exponent \) — How many times the base is multiplied by itself

Explanation: For example, 2^3 means 2 × 2 × 2 = 8. The exponent can be any real number, including fractions and negative numbers.

3. Mathematical Explanation

Details: Exponentiation follows specific mathematical rules:

• Any number to the power of 0 equals 1
• Negative exponents represent reciprocals (x⁻ⁿ = 1/xⁿ)
• Fractional exponents represent roots (x^(1/n) = nth root of x)

4. Using the Calculator

Tips: Enter any real number for base and exponent. The calculator will compute the result accurately.

5. Frequently Asked Questions (FAQ)

Q1: What happens with negative exponents?
A: A negative exponent means you take the reciprocal of the base raised to the absolute value of the exponent (e.g., 2⁻³ = 1/2³ = 1/8 = 0.125).

Q2: How does fractional exponents work?
A: Fractional exponents represent roots (e.g., 4^(1/2) = √4 = 2, 8^(1/3) = ∛8 = 2).

Q3: What is 0 to the power of 0?
A: This is mathematically undefined, though some contexts define it as 1.

Q4: Can I use decimal numbers?
A: Yes, both base and exponent can be any real numbers, including decimals.

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