Answer:
[tex]\large\boxed{\sqrt{2^5}}[/tex]
Step-by-step explanation:
[tex]\bigg(2^\frac{1}{2}\cdot2^\frac{3}{4}\bigg)^2\qquad\text{use}\ a^n\cdot a^m\\\\=\bigg(2^{\frac{1}{2}+\frac{3}{4}}\bigg)^2\qquad\left/\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{1\cdot2}{2\cdot2}+\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{5}{4}\right/\\\\=\bigg(2^\frac{5}{4}\bigg)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{\frac{5}{4}\cdot2}\\\\=2^{\frac{5}{2}}\qquad\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\=\sqrt{2^5}[/tex]
