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MathidiaMathematics Academy
Indices and surds
Lesson 10 of 14
Standard practice

Negative and fractional indices

Objective. Evaluate expressions with negative and fractional powers.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: 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).

2/3
Fraction bar showing 2 out of 3 parts shaded
  1. 1Cube root of 8 is 2.
  2. 22² = 4.
  3. 3The negative index means take the reciprocal: 1/4.

Answer: 1/4

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Common mistake. Treating a negative index as a negative answer.

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