Professional Exponent Calculator

Calculate exponents, powers, square roots, cube roots, and nth roots. Supports positive, negative, and fractional exponents.

Calculator

Can be positive, negative, or fractional

Enter base and exponent to calculate powers, or base and root index to calculate roots.

Complete User Guide

What is an Exponent Calculator?

An exponent calculator computes the result of raising a base number to a power (exponent). It also calculates roots, which are the inverse operation of exponentiation.

This calculator supports positive, negative, and fractional exponents, as well as various types of roots including square roots, cube roots, and nth roots.

How to Use This Calculator

  1. Select calculation type: Exponent (power) or Root
  2. For exponent: Enter base and exponent (can be positive, negative, or fractional)
  3. For root: Enter base and root index (2 for square root, 3 for cube root, etc.)
  4. Click Calculate to get the result with step-by-step solution
  5. Review the result, scientific notation, visualization, and detailed explanation

Understanding Exponents and Roots

Positive Exponents

A positive exponent means multiplying the base by itself that many times. Example: 2³ = 2 × 2 × 2 = 8.

Negative Exponents

A negative exponent means taking the reciprocal. Example: 2⁻³ = 1/(2³) = 1/8 = 0.125.

Fractional Exponents

A fractional exponent represents a root. Example: 8^(1/3) = ∛8 = 2 (cube root of 8).

Roots

A root is the inverse of exponentiation. Square root (√) is the 2nd root, cube root (∛) is the 3rd root, etc.

Examples

Example 1: Positive Exponent

Base: 2, Exponent: 3

Result: 2³ = 8

Example 2: Negative Exponent

Base: 2, Exponent: -3

Result: 2⁻³ = 0.125

Example 3: Square Root

Base: 16, Root Index: 2

Result: √16 = 4

Example 4: Cube Root

Base: 8, Root Index: 3

Result: ∛8 = 2

Important Notes

  • Zero raised to a negative power is undefined.
  • Even roots of negative numbers are not real numbers (they are complex).
  • Odd roots of negative numbers are real numbers (e.g., ∛(-8) = -2).
  • Very large exponents may result in overflow (result too large to represent).

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