Exponential Function, Help Appreciated :-)

Question

my text book asks me to 'Simplify, and express in terms of positive indices'. But my answer always seems to come up with: $x^{\frac {35} {36}}$. The term is

$$\frac{ (x^{-\frac 1 2})^{\frac 2 3} \ x^{\frac 2 3}}{x^{-\frac 3 4}} $$

Answer 1

$$ \frac{ (x^{-\frac 1 2})^{\frac 2 3} \ x^{\frac 2 3}}{x^{-\frac 3 4}} = \frac{ x^{-\frac 1 3} \ x^{\frac 2 3}}{x^{-\frac 3 4}} = \frac{ x^{\frac 1 3} }{x^{-\frac 3 4}} = x^{\frac 1 3} x^{\frac 3 4} = x^{\frac 4 {12}} x^{\frac 9 {12}} = x^{\frac {13} {12}}.$$

Answer 2

You are supposed to use that $$\tag{1} x^a\cdot x^b =x^{a+b}$$

$$\tag{2} (x^a)^b =x^{ab}$$

$$\tag{3} x^{-a}=\frac{1}{x^a}$$

Answer 3

or alternatively $$x^{-1/3}\cdot x^{2/3}\cdot x^{3/4}=x^{13/12}$$