Overview

Exponentiation is a mathematical operation that represents repeated multiplication of a number by itself.

  • x^y: General power operation, calculates x raised to the power y
  • : Square operation, calculates x raised to the power 2
  • : Cube operation, calculates x raised to the power 3
  • e^x: Natural exponential, calculates e raised to the power x

Syntax

x^y // Calculate x raised to the power y
x^2 // Calculate x squared
x^3 // Calculate x cubed
e^x // Calculate e raised to the power x

Examples

Example 1: Calculate 2 to the power 10
Input: 2^10
Result: 1024
Example 2: Calculate 5 squared
Input: 5^2
Result: 25
Example 3: Calculate 4 cubed
Input: 4^3
Result: 64
Example 4: Calculate e squared
Input: e^2
Result: 7.389...
Example 5: Calculate negative exponent
Input: 2^-3
Result: 0.125
2⁻³ = 1/8 = 0.125
Example 6: Calculate fractional exponent
Input: 8^(1/3)
Result: 2
The cube root of 8 equals 2

Important Notes

  1. Non-integer powers of negative numbers may produce complex results
  2. 0 to the power 0 is mathematically debated, typically defined as 1
  3. Negative numbers raised to even powers give positive results
  4. Power operations are right-associative: 2^3^2 = 2^(3^2) = 2^9 = 512