\(\dfrac{2^{15}\cdot9^4}{6^8\cdot8^3}=\dfrac{2^{15}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^8\cdot\left(2^3\right)^3}=\dfrac{2^{15}\cdot3^8}{2^8\cdot3^8\cdot2^9}=\dfrac{2^{15}\cdot3^8}{2^{17}\cdot3^8}=\dfrac{1}{2^2}=\dfrac{1}{4}\)
\(\dfrac{2^{15}.9^4}{6^8.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^8.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{2^8.3^8.2^9}=\dfrac{2^{15}}{2^{17}}=\dfrac{1}{2^2}=\dfrac{1}{4}\)