Question

вычислите наиболее рациональным способом:

(-3)²·15³·(-25)

_____________.

 5⁴·3⁶

Answer 1

=(3²·(5·3)³·(-5²)):(5⁴·3⁶)=-(3²·5³·3³·5²):(5⁴·3⁶)=-(3⁵·5⁵):(5⁴·3⁶)=-(3⁵:3⁶)·(5⁵:5⁴)=

=-⅓·5=-5/3

Ответ:   -5/3.

Answer 2

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

 

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