\[\frac{7^{2} \cdot 7^{9}}{\left( 7^{4} \right)^{2}} - 17^{2} + 27^{0} = \frac{7^{11}}{7^{8}} - 289 + 1 =\]
\[= 7^{3} - 288 = 343 - 288 = 55.\]
\[Ответ:2)\ 55.\]