[tex]\dfrac{1}{5}\cdot[-\dfrac{25^{3}\cdot(125^{4}:5^{7})^{3}}{625^{2}}]=-\dfrac{(5^{2})^{3}\cdot((5^{3})^{4}:5^{7})^{3}}{5\cdot(5^{4})^{2}} =-\frac{5^{6}\cdot(5^{12}:5^{7})^{3}}{5\cdot5^{8}}=\\\\\\= -\frac{5^{6}\cdot(5^{5})^{3}}{5^{9}}=-\dfrac{5^{6}\cdot5^{15}}{5^{9}}=-\dfrac{5^{21}}{5^{9}} = -5^{12}=-244 140 625[/tex]
Wyjaśnienie
Wykorzystano własności potęg:
[tex](a^{m})^{n} = a^{m\cdot n}\\\\a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}[/tex]
