Question

Вычислите
12^2 × 4^3 × 6^2/ 8^2 × 18^3

Answer 1

$\dfrac{12^2\cdot 4^3\cdot 6^2}{8^2\cdot 18^3}=\dfrac{(2^2\cdot 3)^2\cdot (2^2)^3\cdot (2\cdot 3)^2}{(2^3)^2\cdot (2\cdot 3^2)^3}=\dfrac{2^4\cdot 3^2\cdot 2^6\cdot 2^2\cdot 3^2}{2^6\cdot 2^3\cdot 3^6}=\\\\\\=\dfrac{2^{12}\cdot 3^4}{2^9\cdot 3^6}=\dfrac{2^3}{3^2}=\dfrac{8}{9}$