Вычислите: (5^9*10^9)/(2^9*25^9)*(5*2^32-8*2^29)/4^16.

\[\frac{5^{9} \cdot 10^{9}}{2^{9} \cdot 25^{9}} \cdot \frac{5 \cdot 2^{32} - 8 \cdot 2^{29}}{4^{16}} =\]

\[= \frac{\left( 5^{9} \cdot 2^{9} \cdot 5^{9} \right)}{2^{9} \cdot \left( 5^{2} \right)^{9}} \cdot \frac{5 \cdot 2^{32} - 2^{3} \cdot 2^{29}}{\left( 2^{2} \right)^{16}} =\]

\[= \frac{5^{18}}{5^{18}} \cdot \frac{2^{32}(5 - 1)}{2^{32}} = 4.\]