Simplify an expression (DSE wording: "express your answer with positive indices")

Steps

1. Deal with the numbers first.
2. Remove brackets: raise every factor inside to the power.
3. Collect each letter: add indices when multiplying, subtract when dividing.
4. Move any negative index to the other side of the fraction line, so all indices are positive.

Worked examples

(2a³b⁻²)² = 4a⁶b⁻⁴                square every factor
4a⁶b⁻⁴ ÷ 4a⁻¹b = a^(6−(−1)) b^(−4−1)
               = a⁷ b⁻⁵
               = a⁷ / b⁵          positive indices

For the whole topic, read Indices and scientific notation: key points, common mistakes and how the DSE tests it.

Other methods in this topic