Originally Posted by

**mabentley** Hello everyone,

Please could somebody kindly explain what I'm doing wrong here. I have to simplify:

$\displaystyle 2^{-{3/2}}+2^{-{1/2}}+2^{{1/2}}+2^{{3/2}}$

My approach so far is:

$\displaystyle =(\frac{1}{\sqrt{2^{3}}}+\frac{1}{\sqrt{2}}+\sqrt{ 2}+\sqrt{2^{3}})$

$\displaystyle =(\frac{1}{2\sqrt{2}}+\frac{1}{\sqrt{2}}+\sqrt{2}+ 2\sqrt{2})$

... and then I've tried various methods involving simplifying each of the terms, but none of them leads to the correct answer which should be:

$\displaystyle =\bigg(\frac{15}{4}\bigg)\sqrt{2}$