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: 2yfrac(-3)(2)