Exponent Calculator

About the Exponent Calculator

An exponent calculator is a tool that helps you compute the value of a number raised to a power. Exponentiation is a mathematical operation that involves two numbers, the base (x) and the exponent (n), written as xⁿ. The exponent indicates how many times the base is multiplied by itself.

How to Calculate Exponents

Exponentiation is calculated using the following formula:

xⁿ = x × x × ... × x (n times)

Examples:

• 2³ = 2 × 2 × 2 = 8
• 5² = 5 × 5 = 25
• 10⁴ = 10 × 10 × 10 × 10 = 10,000

Fractional Exponents

A fractional exponent represents both a power and a root. The numerator of the fraction indicates the power, and the denominator indicates the root. The formula is:

x^m/n = (x^1/n)^m = (n√x)^m

Examples:

• 8^1/3 = ∛8 = 2
• 16^3/4 = (∜16)³ = 2³ = 8

Negative Exponents

A negative exponent represents the reciprocal of the positive exponent. The formula is:

x^-n = 1 / xⁿ

Examples:

• 2^-3 = 1 / 2³ = 1/8 = 0.125
• 5^-2 = 1 / 5² = 1/25 = 0.04

Exponent Rules

There are several important rules that govern the behavior of exponents:

• Product Rule: x^a × x^b = x^a+b
• Quotient Rule: x^a ÷ x^b = x^a-b
• Power Rule: (x^a)^b = x^a×b
• Zero Exponent: x⁰ = 1 (for x ≠ 0)
• One Exponent: x¹ = x