Ans: B
$\begin{array}{rcl}
\left(\dfrac{1}{9}\right)^{500} (3^{500})^3 & = & 9^{-500} \times 3^{3\times 500} \\
& = & (3^2)^{-500} \times 3^{1500} \\
& = & 3^{2\times (-500)} \times 3^{1500} \\
& = & 3 ^{-1000+1500} \\
& = & 3^{500}
\end{array}$
$\begin{array}{rcl}
\left(\dfrac{1}{9}\right)^{500} (3^{500})^3 & = & 9^{-500} \times 3^{3\times 500} \\
& = & (3^2)^{-500} \times 3^{1500} \\
& = & 3^{2\times (-500)} \times 3^{1500} \\
& = & 3 ^{-1000+1500} \\
& = & 3^{500}
\end{array}$
