Power terms in an algebraic expression are not limited to positive integers.

The terms `x^frac(1)(2)`, `x^-3` and `x^0` are all valid terms.

The rules for manipulating power terms are the same as the rules for manipulating power terms in number (the Laws of Indices).

Note that `x^0` is equal to 1, and that `x^1` is equal to `x`.

Calculate `3x^frac(1)(2) xx 4x^-2`

`3x^frac(1)(2) xx 4x^-2`

`= 3 xx 4 xx x^frac(1)(2) xx 4x^-2`

`=12 xx x^((frac(1)(2)-2))`

`=12x^frac(-3)(2)`

Answer: `12x^frac(-3)(2)`

Simplify `8x^{frac(-3)(2)}y^{frac(1)(2)} \div 2x^frac(-3)(2) y^2`

`8x^{frac(-3)(2)}y^{frac(1)(2)} \div 2x^frac(-3)(2) y^2`

`= 4x^{(frac(-3)(2) - frac(-3)(2))}y^{(frac(1)(2) - 2)}` (add/subtract indices on terms)

`= 4x^0y^frac(-3)(2)` (the first fraction evaluates to zero)

`= 4y^frac(-3)(2)` (`x^0 = 1)`

Answer: 2y^{frac(-3)(2)}

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