Negative Exponents

Free interactive math game: Negative Exponents — 2⁻³ = 1/8. Part of the Powers & Roots category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. 6^(−1) = ?
  2. 2^(−1) = ?
  3. 5^(−2) = ?
  4. 2^(−2) = ?

About this exercise

What a negative exponent means.

How to solve it

A negative exponent gives the reciprocal of the matching positive power, so it moves the value underneath a 1 rather than making it negative.

Worked example

2 to the power -3 is 1 divided by 2 cubed, which is 1 over 8.

Common mistake

Expecting a negative answer. A negative exponent shrinks a positive base towards zero but never carries it below zero.