\(\dfrac{9^4.2^{15}}{2^6.24^3}\) = \(\dfrac{9^4.2^9}{24^3}\) = \(\dfrac{2^9.3^8}{2^9.3^3}\) = 35 = 243
\(\dfrac{9^4\cdot2^{15}}{2^6\cdot24^3}=\dfrac{\left(3^2\right)^4\cdot2^{15}}{2^6\cdot\left(8\cdot3\right)^3}=\dfrac{3^8\cdot2^{15}}{2^6\cdot8^3\cdot3^3}=\dfrac{3^8\cdot2^{15}}{2^6\cdot2^9\cdot3^3}=\dfrac{3^8\cdot2^{15}}{2^{15}\cdot3^3}=3^5=243\)