The simplest way to do this is the use the "laws of exponents"- in particular the fact that $\displaystyle x^{ab}= (x^a)^b$. Here, you have $\displaystyle 2^{5/2)= 2^{5(1/2)}= (2^{1/2})^5$ and $\displaystyle 2^{3/2}= 2^{3(1/2)}= (2^{1/2}^3$. We can write the expression as $\displaystyle (2^{1/2})^5- (2^{1/2})^3$ and factor out $\displaystyle (2^{1/2})^3$ ($\displaystyle 2^{5/2}= 2^{3/2+ 2/2}= 2^{1+ 3/2}$.)
$\displaystyle 2^{5/2}- 2^{3/2}= (2^{3/2})(2- 1)= 2^{3/2}$.