вычислите наиболее рациональным способом: (-3)²·15³·(-25) _____________. 5⁴·3⁶

$\frac{(-3)^{2}\cdot15^{3}\cdot(-25)}{5^{4}\cdot3^{6}}=\frac{-(3^{2}\cdot(3\cdot5)^{3}\cdot5^{2})}{5^{4}\cdot3^{6}}=\frac{-(3^{2}\cdot3^{3}\cdot5^{3}\cdot5^{2})}{5^{4}\cdot3^{6}}=$

$=\frac{-(3^{2}\cdot3^{3})\cdot(5^{3}\cdot5^{2})}{5^{4}\cdot3^{6}}=\frac{-(3^{(2+3)})\cdot(5^{(3+2)})}{5^{4}\cdot3^{6}}=\frac{-(3^{5}\cdot5^{5})}{5^{4}\cdot3^{6}}=-\frac{5}{3}=-1\frac{2}{3}$