1. What is the Power Function?

The power function is a mathematical function of the form y = x^a where x is the base and a is the exponent. It represents repeated multiplication when the exponent is a positive integer.

2. How Does the Calculator Work?

The calculator uses the power function formula:

Where:

• \( x \) — Base value
• \( a \) — Exponent value
• \( y \) — Result of x raised to the power of a

Explanation: The function calculates the result of multiplying x by itself a times (for positive integers) or uses logarithmic calculation for non-integer exponents.

3. Applications of Power Function

Details: Power functions are used in physics (inverse square law), finance (compound interest), biology (allometric scaling), and many other scientific fields.

4. Using the Calculator

Tips: Enter any real number for the base and exponent. The calculator handles both positive and negative values, as well as fractional 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 (x^0 = 1). 0^0 is undefined.

Q2: Can I use negative exponents?
A: Yes, a negative exponent represents the reciprocal (x^-a = 1/(x^a)).

Q3: What about fractional exponents?
A: Fractional exponents represent roots (x^(1/a) = a-th root of x).

Q4: Are there limitations to this calculator?
A: It may not handle extremely large or small numbers perfectly due to floating-point precision limits.

Q5: What's the difference between pow() and exp()?
A: pow(x,a) calculates x^a while exp(x) calculates e^x (e raised to power x).