Question

Найдите значение выражения:

​

Answer 1

$\displaystyle \frac{5 \times 2 ^{13} \times {4}^{11} - {16}^{9} }{(3 \times 2^{11}) ^{3} } = \frac{5 \times {2}^{13} \times ( {2}^{2})^{11} - ({2}^{4})^{9} }{3^{3} \times {2}^{33} } = \\ = \frac{5 \times {2}^{13} \times {2}^{22} - {2}^{36} }{27 \times {2}^{33} } = \frac{5 \times 2 ^{13 + 22} - {2}^{36} }{27 \times {2}^{33} } = \\ = \frac{5 \times {2}^{35} - {2}^{36} }{27 \times {2}^{33} } = \frac{ {2}^{35} (5 - 2)}{27 \times {2}^{33} } = \\ = \frac{ {2}^{35} \times 3}{27 \times {2}^{33} } = \frac{ {2}^{2} }{9} = \frac{4}{9}$

Успехов