Exponent Calculator
Solve Exponent step by step — enter coefficients or expressions to get roots, factors, or simplified forms with detailed algebraic working.
Formula
x^y
Exponentiation is repeated multiplication. b^n means multiplying b by itself n times.
Worked Examples
Example 1: Cube
Problem:2^3
Solution:2 × 2 × 2
Result:8
Example 2: Negative Power
Problem:2^-2
Solution:1 / (2^2) = 1/4
Result:0.25
Example 3: Square Root
Problem:9^(0.5)
Solution:√9
Result:3
Frequently Asked Questions
What does a negative exponent mean?
A negative exponent indicates the reciprocal. x^-n equals 1 divided by x^n.
What is a fractional exponent?
Fractional exponents represent roots. x^(1/n) is the nth root of x. x^(1/2) is the square root.
How do exponents relate to logarithms?
Logarithms are the inverse of exponentiation. If b^x = y, then log_b(y) = x.
Background & Theory
**Exponentiation:**
Exponentiation is a mathematical operation involving two numbers, the base (b) and the exponent (n). It is written as **bⁿ**.
* **bⁿ**: "b raised to the power of n"
* Definition: Multiply 'b' by itself 'n' times.
**Rules:**
* **Product Rule:** aᵐ × aⁿ = aᵐ⁺ⁿ
* **Quotient Rule:** aᵐ / aⁿ = aᵐ⁻ⁿ
* **Power Rule:** (aᵐ)ⁿ = aᵐⁿ
* **Negative Exponent:** a⁻ⁿ = 1/aⁿ
* **Zero Exponent:** a⁰ = 1 (for a ≠ 0)
**Roots:**
The nth root of a number x is a number r which, when raised to the power n, yields x.
* **ⁿ√x = r ⟺ rⁿ = x**
History
The concept of powers dates back to ancient Babylonians, who used squares and cubes. The modern notation for exponents (xʸ) was introduced by Rene Descartes in 1637 in his work "La Geometrie." Before that, mathematicians used cumbersome words or symbols to describe repeated multiplication.