Answer:
Given the expression: [tex](2^{\frac{1}{2}} \times 2^{\frac{3}{4}})^2[/tex]
Using:
[tex](2^{\frac{1}{2}+\frac{3}{4}} )^2[/tex]
Simplify:
[tex](2^{\frac{5}{4}})^2[/tex]
[tex]2^{\frac{5 \times 2}{4}} =2^{ \frac{5}{2}}[/tex] = [tex]\sqrt[2]{2^5} = \sqrt[2]{32} = 4\sqrt{2}[/tex]
Therefore, the expression which is equivalent to [tex](2^{\frac{1}{2}} \times 2^{\frac{3}{4}})^2[/tex] is: [tex]4\sqrt{2}[/tex] or [tex]2^{\frac{5}{2} }[/tex]
