Negative Exponent Calculator

Calculate negative exponents (x-n = 1/xn) and explore fractional results

Input Parameters

Note: Enter a positive value, and the calculator will automatically apply the negative sign.

Calculation Results

Calculation Formula

x-n = 1/xn

Where:
x = base value
n = absolute value of exponent

Result

Enter values and click Calculate to see result

Negative Exponent Calculator Calculator Usage Guide

Learn how to use the Negative Exponent Calculator and understand the mathematical principles behind it

How to Use This Calculator

  1. Enter the base value (x) in the first input field. This can be any real number including fractions.
  2. Enter the exponent (n) in the second input field. For negative exponents, enter a positive value (the calculator will automatically apply the negative sign).
  3. Click the "Calculate" button to compute the result.
  4. The calculator will display the result in both decimal and simplified forms.

Understanding Negative Exponents

A negative exponent represents the reciprocal of the base raised to the absolute value of the exponent:

x-n = 1/xn

For example:

  • 2-3 = 1/23 = 1/8 = 0.125
  • 5-2 = 1/52 = 1/25 = 0.04
  • (1/3)-4 = 34 = 81

Mathematical Principles

Negative exponents were introduced to simplify expressions with fractions. The rule x-n = 1/xn allows us to write:

1/(xn) = x-n

This property is particularly useful in scientific notation and algebraic manipulations. The calculator handles very large and very small results by displaying them in scientific notation when appropriate.