I am doing this question, and I need to simplify the following in order for me to complete the question. Have I done anything wrong below?
Given $\left(\frac{1}{7\alpha\sqrt\pi}\right)^{1/2}$, $\alpha=\sqrt{\frac{h}{mw}}$, am I correct to simplify it to:
$$\left(\frac{1}{7\sqrt{\frac{h\pi}{mw}}}\right)^{1/2}$$
and can I write it as:
$$\frac{1}{\sqrt7}\left(\frac{1}{\sqrt{\frac{h\pi}{mw}}}\right)^{1/2}$$ and further simplifying it: $$\frac{1}{\sqrt7}\left(\left({{\frac{h\pi}{mw}}}\right)^{-1/2}\right)^{1/2}$$ $$\frac{1}{\sqrt7}\left({{\frac{h\pi}{mw}}}\right)^{-1/4}$$ $$\frac{1}{\sqrt7}\left(\frac{1}{\left({{\frac{h\pi}{mw}}}\right)^{1/4}}\right)$$ $$\frac{1}{\sqrt7}\left(\frac{1}{\left({{\frac{h\pi}{mw}}}\right)}\right)^{1/4}$$ $$\frac{1}{\sqrt7}\left(\frac{mw}{h\pi}\right)^{1/4}$$