Answer: [tex]\sqrt{32}[/tex]
Step-by-step explanation:
Assuming the described expression is:
[tex](2^{\frac{1}{2}} 2^{\frac{3}{4}})^{2}[/tex]
Since we have the same base, we can add the exponents:
[tex](2^{\frac{5}{4}})^{2}[/tex]
Multiplying the exponents:
[tex]2^{\frac{10}{4}}[/tex]
Simplifying the fraction in the exponent:
[tex]2^{\frac{5}{2}}=\sqrt{2^{5}}[/tex]
Finally the expression is equivalent to:
[tex]\sqrt{32}[/tex]
