Answer
$42$
Work Step by Step
Given: $\quad5^\left(\log _{5} 6+\log _{5} 7\right)$
Use the rule $\log A+\log B=\log (A B)$ to obtain:
$$5^\left(\log _{5} 6+\log _{5} 7\right)=5^{\log _{5}(6 \times 7)}=5^{ \log _{5}{42}}$$
Using the rule $a^{\log _{a} M}=M$ gives
$$5^{\log _{5} 42}=42$$
