Задача 41. Вычислите    \(\dfrac{{{{24}^4}}}{{{2^6} \cdot {3^3}}}:\dfrac{{{{20}^4}}}{{{2^5} \cdot {5^6}}} + \dfrac{{{{21}^8} \cdot {4^6}}}{{{3^{18}} \cdot {7^5}}}:\dfrac{{{8^5} \cdot {{49}^3}}}{{{{14}^4} \cdot {9^5}}}\)

Ответ

ОТВЕТ: 614.

Решение

\(\dfrac{{{{24}^4}}}{{{2^6} \cdot {3^3}}}:\dfrac{{{{20}^4}}}{{{2^5} \cdot {5^6}}} + \dfrac{{{{21}^8} \cdot {4^6}}}{{{3^{18}} \cdot {7^5}}}:\dfrac{{{8^5} \cdot {{49}^3}}}{{{{14}^4} \cdot {9^5}}} = \dfrac{{{3^4} \cdot {8^4}}}{{{2^6} \cdot {3^3}}} \cdot \dfrac{{{2^5} \cdot {5^6}}}{{{4^4} \cdot {5^4}}} + \dfrac{{{3^8} \cdot {7^8} \cdot {4^6}}}{{{3^{18}} \cdot {7^5}}} \cdot \dfrac{{{2^4} \cdot {7^4} \cdot {9^5}}}{{{2^{15}} \cdot {7^6}}} = \)

\( = \dfrac{{{3^4}}}{{{3^3}}} \cdot \dfrac{{{2^{12}} \cdot {2^5}}}{{{2^6} \cdot {2^8}}} \cdot \dfrac{{{5^6}}}{{{5^4}}} + \dfrac{{{3^8} \cdot {3^{10}}}}{{{3^{18}}}} \cdot \dfrac{{{7^8} \cdot {7^4}}}{{{7^5} \cdot {7^6}}} \cdot \dfrac{{{2^{12}} \cdot {2^4}}}{{{2^{15}}}} = 3 \cdot {2^3} \cdot {5^2} + {3^0} \cdot 7 \cdot 2 = 3 \cdot 8 \cdot 25 + 14 = 614.\)

Ответ:  614.