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**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

- Multiplication Rule n
- 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.

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