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Powers and indices
Years 6 to 10
A power tells you how many times to multiply a number by itself, and the index laws make working with powers quick.
For learners
2³ means 2 × 2 × 2 = 8. The small 3 is the power, or index. It says how many 2s to multiply.
To multiply powers of the same number, add the powers. 2³ × 2² = 2⁵, because three 2s and two 2s make five 2s.
To divide, subtract the powers. And any number to the power 0 is 1.
A worked example
Simplify .
- The bases are the same, so add the powers.
- .
- The answer is .
For grown-ups
Write powers out in full until the laws make sense: 2³ × 2² = (2 × 2 × 2) × (2 × 2). The laws only work when the bases are the same. Negative powers give fractions, and fractional powers give roots.
Common mistakes
- Thinking 2³ means 2 × 3.
- Multiplying the powers instead of adding them (2³ × 2² is not 2⁶).
- Applying the laws when the bases are different.
Why it matters
Powers describe fast growth, such as bacteria, savings with interest and the size of computer storage.
Topics in quarter that use this
- Laws of indices
- Simplifying surds
- Growth and decay
- Logarithms and their laws