Answer
$8\log_2{a}+2\log_2{b}$
Work Step by Step
The given expression can be re-arranged as:
$ \log_2 [(a^2)^4(\sqrt{b})^4] =\log_2{(a^8b^2)}$
Use $\log_a{(mn)}=\log_a{m} + \log_a{n}$ to obtain:
$\log_2{\left(a^8b^2\right)}=\log_2{\left(a^8\right)}+\log_2{(b^2)}$
Use $\log_a{a^m}=m\log_a{m}$ to obtain:
$ \log_2{(a^8)}+\log_2{(b^2)}=8\log_2{a}+2\log_2{b}$
