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.