Задача 42. Вычислите    \(\dfrac{{{{12}^6}}}{{{4^9} \cdot {9^3}}} \cdot \dfrac{{{{40}^5}}}{{{2^8} \cdot {5^4}}} + \dfrac{{{{16}^3} \cdot {3^{21}}}}{{{2^8} \cdot {5^6}}}:\dfrac{{{{18}^{10}}}}{{{2^7} \cdot {5^8}}}\)

Ответ

ОТВЕТ: 160.

Решение

\(\dfrac{{{{12}^6}}}{{{4^9} \cdot {9^3}}} \cdot \dfrac{{{{40}^5}}}{{{2^8} \cdot {5^4}}} + \dfrac{{{{16}^3} \cdot {3^{21}}}}{{{2^8} \cdot {5^6}}}:\dfrac{{{{18}^{10}}}}{{{2^7} \cdot {5^8}}} = \dfrac{{{4^6} \cdot {3^6}}}{{{4^9} \cdot {3^6}}} \cdot \dfrac{{{8^5} \cdot {5^5}}}{{{2^8} \cdot {5^4}}} + \dfrac{{{2^{12}} \cdot {3^{21}}}}{{{2^8} \cdot {5^6}}} \cdot \dfrac{{{2^7} \cdot {5^8}}}{{{2^{10}} \cdot {9^{10}}}} = \)

\( = \dfrac{{{2^{12}} \cdot {2^{15}}}}{{{2^{18}} \cdot {2^8}}} \cdot \dfrac{{{5^5}}}{{{5^4}}} + \dfrac{{{2^{12}} \cdot {2^7}}}{{{2^8} \cdot {2^{10}}}} \cdot \dfrac{{{3^{21}}}}{{{3^{20}}}} \cdot \dfrac{{{5^8}}}{{{5^6}}} = 2 \cdot 5 + 2 \cdot 3 \cdot 25 = 10 + 150 = 160.\)

Ответ:  160.