[tex] (3^{19} $\cdot$ 25^{9} )^{2} : 15^{36} = (3^{19} $\cdot$ 5^{2\cdot9} )^{2}:15^{36} = 3^{19\cdot2} $\cdot$ 5^{2\cdot9\cdot2}: 15^{36} = \\ = 3^{38} $\cdot$ 5^{36} : 15^{36} = 3^{38}\cdot (5:15)^{36} = 3^{38} \cdot(1:3)^{36} = \\ = 3^{38} : 3^{36} = 3^{2} =9[/tex]
