Indices and Surds AS Mathematics

Prerequisite Knowledge

  • Know and apply the following rules of indices:
    • Multiplication Rule na × nb = na + b
    • Division Rule  na × nb = na + b
    • Power Rule (na)b
    • Power of Zero
  • Evaluate expressions with fractional and negative powers
  • Simplify a surd
  • Rationalise a denominator in the form 1/√a

Success Criteria

  • Understand and be able to use the laws of indices for all rational exponents.
  • Use and manipulate surds, including rationalising the denominator.

Teaching Points

  • Simplifying surds at the start of a problem often makes future working much simpler.
  • Students need to:
    • evaluate expressions involving numerical and algebraic bases with a fractional and negative power.
    • apply the rules of indices to fractional and negative powers.
    • know how the complex conjugate is used to rationalise a denominator.


  • Students often leave surds un-simplified especially when rationalising a denominator using the complex conjugate.
  • 1/2x is often written incorrectly written as 2x-1 rather than (2x)-1.
  • √a + √b is often incorrectly simplified to √(a +b)
  • Students often struggle to evaluate indices involving both a fractional and negative power.  This is especially true when the base involves an algebraic and numerical term.

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