Własności działań na potęgach: [latex]a^{n}*a^{m}=a^{n+m}\ a^{n}:a^{m}=a^{n-m}\ (a^{n})^{m}=a^{n*m}\ a^{-n}=(frac{1}{a})^{n}\ a^{n}*b^{n}=(ab)^{n} [/latex] =============================================== [latex]25^{8}x=frac{5^{16}-5^{15}}{125^{2}*25^{-frac{7}{2}}}\ (5^{2})^{8}x=frac{5^{15}*(5-1)}{(5^{3})^{2}*(5^{2})^{-frac{7}{2}}}\ 5^{2*8}x=frac{5^{15}*4}{5^{3*2}*5^{2*-frac{7}{2}}}\ 5^{16}x=frac{5^{15}*4}{5^{6}*5^{-7}}\ 5^{16}x=frac{4*5^{15}}{5^{6-7}}\ 5^{16}x=frac{4*5^{15}}{5^{-1}}\ 5^{16}x=4*5^{15}:5^{-1}\ 5^{16}x=4*5^{15+1}\ 5^{16}x=4*5^{16} |:5^{15}\ x=4[/latex]
