Question

Which expression is equivalent to (2^1/2 x 2^3/4)^2

Answer 1

(2^1/2 x 2^3/4)^2
= (2^2/4 x 2^3/4)^2
= (2^5/4)^2
= 2^10/4
= 2^5/2

Answer 2

Answer:

Given the expression: $(2^{\frac{1}{2}} \times 2^{\frac{3}{4}})^2$

Using:

• $a^n \times a^m = a^{n+m}$

• $(a^n)^m = a^{nm}$
• $a^{\frac{m}{n}} = \sqrt[n]{a^m}$

$(2^{\frac{1}{2}+\frac{3}{4}} )^2$

Simplify:

$(2^{\frac{5}{4}})^2$

$2^{\frac{5 \times 2}{4}} =2^{ \frac{5}{2}}$ = $\sqrt[2]{2^5} = \sqrt[2]{32} = 4\sqrt{2}$

Therefore, the expression which is equivalent to  $(2^{\frac{1}{2}} \times 2^{\frac{3}{4}})^2$ is: $4\sqrt{2}$ or $2^{\frac{5}{2} }$