Sorry for the formatting of the maths, I dont know why its bunching up. Tried to add the multiplication sign in to make it more readable.
So the question was:
\begin{equation} \frac{x^{-7}\cdot y^2}{(\sqrt[4]{x}\cdot z)^6 } \end{equation}
when written in the form $x^ay^bz^c$ what is the value of $a$?
I first calculated it as $17/2$:
\begin{equation} \frac{x^{-7}\cdot y^2}{(\sqrt[4]{x})^6\cdot (z)^6 }\longrightarrow \end{equation}
\begin{equation} \frac{x^{-7}\cdot y^2}{(x^\frac{3}{2})(z)^6 }\longrightarrow \end{equation}
then by dividing the x values:
\begin{equation}x^\frac{17}{2}y^2 z^6 \end{equation}
but then by using simple exponent rules (ie. $x^{m-n}$ ) I ended up getting $x^{-\frac{17}{2}}$.
Which one of these answers is correct (if either is). If neither are could you please tell me the correct way?
-17/2 is correct. In your first answer, the exponent corresponding to z should be -6 as it is in the denominator. Once you realise why it is -6 and not 6 for z then same applies to x