Hello, metaname90!
$\displaystyle \text{Solve for }r\!:\;\;2^{3\log_4(3)} \:=\:\sqrt{r}$
The left side is: .$\displaystyle 2^{\log_4(3^3)} \;=\;2^{\log_4(27)}$
Since $\displaystyle 2 = 4^{\frac{1}{2}} $
. . we have: .$\displaystyle (4^{\frac{1}{2}})^{\log_4(27)} \;=\; 4^{\frac{1}{2}\log_4(27)} \;=\;4^{\log_4(27^{\frac{1}{2}})} \;=\;27^{\frac{1}{2}} $
The equation becomes: .$\displaystyle 27^{\frac{1}{2}} \:=\:r^{\frac{1}{2}} \quad\Rightarrow\quad r \:=\:27$