Question

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

Answer 1

2

Explanation:

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