[tex]\dfrac{125^{9}\div 25^{2} }{125^{3}\cdot 5^{7} \cdot 125^{6} } =\dfrac{(5^{3} )^{9}\div (5^{2} )^{2} }{(5^{3} )^{3}\cdot 5^{7} \cdot (5^{3} )^{6} }=\dfrac{5^{3\cdot 9}\div 5^{2\cdot 2} }{5^{3\cdot 3}\cdot 5^{7} \cdot 5^{3\cdot6} } =\dfrac{5^{27}\div 5^{4} }{5^{9}\cdot 5^{7} \cdot 5^{18} } =\dfrac{5^{27-4} }{5^{9+7+18} } =\dfrac{5^{23} }{5^{34} } =5^{23-34} =5^{-11}[/tex]
Korzystam ze wzorów:
[tex]x^{n} \cdot x^{m} =x^{n+m} \\\\x^{n} \div x^{m} =x^{n-m} \\\\(x^{n} )^{m} =x^{n\cdot m}[/tex]
