What negative and fractional indices mean, evaluating powers like 8^(−2/3) exactly, and solving equations with the unknown in the index.
What you will learn
- Write a negative index as a reciprocal
- Use fractional indices as roots
- Evaluate a^(m/n) and a^(−m/n) exactly
- Solve equations like 4ˣ = 8
Negative indices mean "one over"
Carry on the pattern 2³ = 8, 2² = 4, 2¹ = 2, 2⁰ = 1: each step divides by 2, so 2⁻¹ = 1/2 and 2⁻³ = 1/8.
a⁻ⁿ = 1/aⁿ
A negative index never makes the answer negative: 5⁻² = 1/25. For a fraction, flip it: (2/3)⁻¹ = 3/2.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Negative indices mean "one over"
- Fractional indices mean roots
- The unknown in the index
- Try it: Check on the calculator
7 practice questions, marked as you go; about 25 minutes in all.
In this unit: Powers, roots and standard form
Squares, cubes and roots, the laws of indices (negative and fractional too), and very large and very small numbers in standard form.
- Powers and roots
- The laws of indices
- Negative and fractional indices
- Standard form
- Calculating with standard form