Indices: negative and fractional
a−n = 1/an; a1/n = n√a; am/n = (n√a)m.
The full set of index laws applied: multiply (add powers), divide (subtract), brackets (multiply), zero power (= 1), negative power (reciprocal), fractional power (root).
Worked examples
2−3 = 1/8.
161/2 = 4, 271/3 = 3.
82/3 = (3√8)2 = 4.
Frequently asked questions
a<sup>0</sup>?
= 1 for any non-zero a. 00 is undefined / a special case.
Negative fractional?
32−2/5 = 1 / 322/5 = 1 / (5√32)2 = 1/4.