If _10a = p, _10b = q, then what is _10 ( a^pb^q ) equal to?

Answer: Option A

$$\begin{array}{rl}& \text{Given},\\ & {\log }_{10}a=p,{\log }_{10}b=q\\ & {\log }_{10}\left(a^p{b}^q\right)={\log }_{10}{a}^p+{\log }_{10}{b}^q\\ & =p{\log }_{10}a+q{\log }_{10}b\\ & =p^2+q^2\end{array}$$