MathsYears 9–11Algebra

Index laws

Learn Index laws for Years 9–11 pupils (ages 13–16). Free practice questions, lessons and worked examples — aligned to the UK National Curriculum.

What you'll learn

  1. 1

    When you multiply powers of the same base you ADD the indices: a³ × a⁴ = a⁷.

  2. 2

    When you divide, you SUBTRACT: a⁷ ÷ a³ = a⁴. When you raise a power to a power, you MULTIPLY: (a³)⁴ = a¹².

  3. 3

    Simplify a⁵ × a³.

  4. 4

    The commonest error is multiplying the indices when you should add. a³ × a⁴ is a⁷, not a¹².

  5. 5

    Simplify (2a³)⁴. The power applies to everything inside: 2⁴ = 16, and (a³)⁴ = a¹². So the answer is 16a¹².

  6. 6

    Simplify (x⁴)³.

  7. 7

    What is a⁰ (where a is not zero)?

Practise Index laws with Whizlo

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