Question

Which expression is equivalent to [4^5/4 4^1/4 / 4^1/2]^1/2 Please quick helppp

Answer 1

Answer:

2

Step-by-step explanation:

$\left(\dfrac{4^\frac{5}{4}\cdot4^\frac{1}{4}}{4^\frac{1}{2}}\right)^\frac{1}{2}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\ \text{and}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\left(4^{\frac{5}{4}+\frac{1}{4}-\frac{1}{2}\right)^\frac{1}{2}=\left(4^{\frac{6}{4}-\frac{1}{2}}\right)^\frac{1}{2}=\left(4^{\frac{3}{2}-\frac{1}{2}}\right)^\frac{1}{2}=\left(4^{\frac{2}{2}\right)^\frac{1}{2}=\left(4^1\right)^\frac{1}{2}\\\\=4^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\=\sqrt4=2$

Answer 2

[4^(5/4+1/4)]^1/2

= --------------------------

4^(1/2 * 1/2)

[4^(6/4)]^1/2

= ----------------------

4^(1/4)

4^(3/2 * 1/2)

= ----------------------

4^(1/4)

4^(3/4)

= ---------------

4^(1/4)

= 4^(3/4 - 1/4)

= 4^2/4

= 4^1/2

= √4

= 2

Answer is C. 2