Ответ:   [tex]\pmb { \dfrac{5}{6}}[/tex]

Объяснение:

[tex]\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}} \\\\ \bigstar \:\: a^n \cdot b^n =(ab)^n \end{minipage}}\end{gathered}[/tex]

Решение :

[tex]\large \boldsymbol{} \displaystyle \frac{(6^3)^3 \cdot 9^2 \cdot (5^2)^2}{1000 \cdot 18^ 7 } = \frac{6^9 \cdot (3^2)^2 \cdot 5^4}{10^3 \cdot (2 \cdot 3^2)^7} = \frac{(2 \cdot 3)^9\cdot 3^4\cdot 5^4 }{(2\cdot 5)^3 \cdot 2^7 \cdot 3^{14 } } = \\\\\\ =\frac{2^9 \cdot 3^9 \cdot 3^4 \cdot 5^4}{2^3 \cdot 5^ 3 \cdot 2^7 \cdot 3^{14} } = \frac{2^9 \cdot 3^{9 + 4 }\cdot 5^4}{2^{3+7}\cdot 3^{14}\cdot 5^3} = \frac{2^9 \cdot 3^{13 }\cdot 5^4}{2^{10}\cdot 3^{14}\cdot 5^3} =[/tex]

[tex]\large \boldsymbol{} \displaystyle = 2^{9-10 }\cdot 3^{13-14}\cdot 5^{4-3} = 5 \cdot 3^{-1}\cdot 2^{-1} = \boxed{\frac{5}{6}}[/tex]