Answer:
2
Step-by-step explanation:
[tex]\left(\dfrac{4^\frac{5}{4}\cdot4^\frac{1}{4}}{4^\frac{1}{2}}\right)^\frac{1}{2}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\ \text{and}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\left(4^{\frac{5}{4}+\frac{1}{4}-\frac{1}{2}\right)^\frac{1}{2}=\left(4^{\frac{6}{4}-\frac{1}{2}}\right)^\frac{1}{2}=\left(4^{\frac{3}{2}-\frac{1}{2}}\right)^\frac{1}{2}=\left(4^{\frac{2}{2}\right)^\frac{1}{2}=\left(4^1\right)^\frac{1}{2}\\\\=4^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\=\sqrt4=2[/tex]
