Mokoro
Digital Growth Engine

Mathematics · Topic

Powers, roots and index laws

Fractional and negative indices are extended-tier items; convert to a root and a power before calculating.

2 original questions in the bank, worth 3 marks · above the two-per-topic floor

Drill this topic All powers, roots and index laws questions

The questions, with the examiner reasoning

Simplify2 marksIGCSE

Simplify (2x³y)² × 3x⁻²y⁴ ÷ 6xy², leaving your answer in terms of x and y.

Show the mark scheme and the examiner note

Answer: 2x³y⁴

  1. Square the bracket: 4x⁶y²
  2. Multiply: 4x⁶y² × 3x⁻²y⁴ = 12x⁴y⁶
  3. Divide: 12x⁴y⁶ ÷ 6xy² = 2x³y⁴

Examiner technique: Work in three lines — bracket, multiply, divide. Learners who try to do it in one line lose the index of x more often than any other single mark in the paper.

Work out1 markIGCSE

Work out 8^(2/3).

Show the mark scheme and the examiner note

Answer: 4

  1. 8^(2/3) means (cube root of 8)²
  2. Cube root of 8 = 2
  3. 2² = 4
  • A. 4 — Correct: the cube root of 8 is 2, and 2² = 4.
  • B. 16 — You squared 8 and then took a root in the wrong order: 8² = 64, and the cube root of 64 is 4.
  • C. 2 — That is the cube root of 8. The numerator of the fraction is still waiting to be applied.
  • D. 5.33 — That is 8 × 2 ÷ 3 — multiplication instead of a power.

Examiner technique: Read a fractional index as "root, then power". Root first is easier arithmetic, and it keeps the numbers small enough to do without a calculator.