Module 7 · Exponents · Lesson 32 of 39

Negative and zero exponents

x⁰ = 1 and a negative exponent means one over.

In this lesson · about 12 minutes

  • Evaluate negative exponents
  • Use the zero exponent rule
  • Simplify with negative exponents

Negative exponent: x−a = 1xa. A negative exponent moves the power to the other side of the fraction bar and makes the exponent positive. 2−3 = 123 = 18. On a fraction, it flips the fraction: (23)−2 = (32)2 = 94.

Zero exponent: any nonzero base to the power 0 is 1. x3x3 = x0, and anything divided by itself is 1.

The quotient rule still works with negatives: x3x−2 = x3−(−2) = x5.

When the bases differ but the exponents match, you can group them: x3y3 = (xy)3.

Try it · interactive

Exponent explorer

Set the exponent to 0, then to negative numbers. The value becomes 1, then fractions.

23 = 8

2 · 2 · 2

2 is used as a factor 3 times.

Loading practice…

Practice sets mastered: 0 of 1

Tip: master each practice set first (get 5 right in a row).

Noviq Academy Pre-Algebra is free and for learning. Practice problems are generated fresh each time; if you think an answer is wrong, tell us through the contact page.