Math Playground
Algebra

Negative exponents

x⁻¹ is 1/x. Negatives in the exponent flip the base over.

A negative exponent means: take the reciprocal.

Try this
-3
2ⁿ = 2^-3 = 1/2^3 = 0.1250

What a negative exponent does

  • x⁻ⁿ = 1/xⁿ — flip the base to the other side of the fraction bar.
  • 1/x⁻ⁿ = xⁿ — flipping twice cancels.
  • It is not a negative number: 2⁻³ = 1/8, which is positive.
Your turn

Write 5⁻² as an ordinary fraction.

Watch out

2⁻³ does not equal −6 or −8. The minus sign is on the *exponent*, telling you to take a reciprocal, not to negate.

Rule
Try it

2⁻³

1/2³ = 1/8.

Negative exponents flip the base over the fraction bar.