Indices and Surds AS Mathematics

Rules of Indices

Expressions with Fractional Powers

Rationalising Denominators

Complex Conjugate

Prerequisite Knowledge

• Know and apply the following rules of indices:
  • Multiplication Rule n^a × n^b = n^{a + b}
  • Division Rule  n^a × n^b = n^{a + b}
  • Power Rule (n^a)^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.

Misconceptions

• 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.