Question

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

Answer 1

Answer:

$\sqrt{2^5}$

Step-by-step explanation:

$2^{1/2}$ × $2^{3/4}$ = $2^{5/4}$

($2^{5/4}$)² = $2^{5/2}$ = $\sqrt{2^5}$

Answer 2

Answer:

$\large\boxed{\sqrt{2^5}}$

Step-by-step explanation:

$\bigg(2^\frac{1}{2}\cdot2^\frac{3}{4}\bigg)^2\qquad\text{use}\ a^n\cdot a^m\\\\=\bigg(2^{\frac{1}{2}+\frac{3}{4}}\bigg)^2\qquad\left/\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{1\cdot2}{2\cdot2}+\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{5}{4}\right/\\\\=\bigg(2^\frac{5}{4}\bigg)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{\frac{5}{4}\cdot2}\\\\=2^{\frac{5}{2}}\qquad\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\=\sqrt{2^5}$