Are you familiar with the rules of exponents? - 1

$\left(\dfrac{8^{-6}\cdot 16^3 \cdot 7^9}{4^{-4}\cdot 3^2 \cdot 49^{-1}}\right)^{-3}$

$=\left(\dfrac{4^{4}\cdot 16^3 \cdot 7^9 \cdot 49}{8^{6}\cdot 3^2}\right)^{-3}=\left(\dfrac{2^{2(4)} \cdot 2^{4(3)} \cdot 7^9 \cdot 7^2}{2^{3(6)} \cdot 3^2}\right)^{-3}=\left(\dfrac{2^8 \cdot 2^{12} \cdot 7^{11}}{2^{18} \cdot 3^2}\right)^{-3}=\left(\dfrac{2^{20} \cdot 7^{11}}{2^{18} \cdot 3^2}\right)^{-3}=\left(\dfrac{2^2 \cdot 7^{11}}{3^2}\right)^{-3}=\dfrac{2^{-6} \cdot 7^{-33}}{3^{-6}}=$ $\boxed{\dfrac{3^6}{2^6 \cdot 7^{33}}}$