<s>[INST] What have I done wrong in solving this problem with indices rules? The question asks to simplify: 
$$\left(\dfrac{25x^4}{4}\right)^{-\frac{1}{2}}.$$
So I used $(a^m)^n=a^{mn}$ to get
$$\dfrac{25}{4}x^{-2} = \dfrac{25}{4} \times \dfrac{1}{x^2} = \frac{25}{4x^2} = \frac{25}{4}x^{-2}$$
However, this isn't the answer, and I can't see what I've done wrong. 
This is what the mark scheme says:
$$\left(\dfrac{25x^4}{4}\right)^{-\frac{1}{2}} = \left[\left(\frac{4}{25x^4}\right)^{\frac{1}{2}} \text{ or } \left(\frac{5x^2}{2}\right)^{-1} \text{ or } \frac{1}{\left(\dfrac{25x^4}{4}\right)^{\frac{1}{2}}}\right] = \frac{2}{5}x^{-2}$$
To me, my answer looks more simple than theirs, and I can't see what I've done wrong.
 [/INST] $$\Big(\frac{25x^4}{4}\Big)^{-\frac{1}{2}}=\Big(\frac{4}{25x^4}\Big)^{\frac{1}{2}}=\frac{4^{\frac{1}{2}}}{25^{\frac{1}{2}}(x^4)^{\frac{1}{2}}}=\frac{2}{5x^2}$$
</s>