Indices and surds
Lesson 10 of 14
Negative and fractional indices
Objective. Evaluate expressions with negative and fractional powers.
The key idea
a⁻ⁿ = 1/aⁿ and a^(1/n) is the nth root of a. Combined, a^(−m/n) is one over the nth root of a, raised to m.
Worked example
Evaluate 8^(−2/3).
- 1Cube root of 8 is 2.
- 22² = 4.
- 3The negative index means take the reciprocal: 1/4.
Answer: 1/4
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Treating a negative index as a negative answer.
Your progress
Tick each step as you finish it — Continue brings you back here.
0 of 5 steps complete