[tex]1)\\x^{3}\cdot(x^{4})^{5}:x^{7} = x^{3}\cdot x^{20} : x^{7} = x^{23}:x^{7} = x^{16}\\\\2) \\(x^{5}\cdot x^{6})^{2} :(x^{14} : x^{11})^{3} = (x^{11})^{2}:(x^{3})^{3} = x^{22}:x^{9} = x^{13}\\\\3)\\((x^{10} :x^{7})^{2}\cdot x^{2}):(x^{12}:x^{9}\cdot x) = [(x^{3})^{2}\cdot x^{2}]:(x^{3}\cdot x) = [(x^{6})\cdot x^{2}]:x^{4} =\\\\=x^{8}:x^{4}=x^{4}[/tex]
[tex]4)\\(a^{3}\cdot a^{5})^{2}:(a^{10} :a^{8})^{5} = (a^{8})^{2}:(a^{2})^{5} = a^{16}:a^{10} = a^{6}\\\\5)\\a^{7}\cdot(a^{10}:a^{5})^{2} :(a^{11}:a^{8})^{4} = a^{7}\cdot(a^{5})^{2}:(a^{3})^{4} = a^{7}\cdot a^{10}:a^{12} =a^{17}:a^{12} = a^{5}[/tex]
Wyjaśnienie:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n}[/tex]
