[tex]6a)\\\\\frac{(a^2)^7:a^4}{aa^6 } = \frac{ a^{14} :a^4}{ a^{1+6} } = \frac{ a^{14-4} }{ a^{7} } = \frac{ a^{10} }{ a^{7} } =a^{10-7}=a^{3}\\\\b)\\\\\frac{ (a^3)^4*(a^2)^5 }{(a^6)^3:a^4}=\frac{ a^ {12}* a^ {10}}{ a^{18} :a^4}=\frac{ a^ {12+10}}{ a^{18-4}}= \frac{ a^ {22}}{ a^{14}}=a^{22-14}=a^8\\\\c)\\\\ \frac{(a^7*a^2)^3}{(a^5*a^3)^2}= \frac{(a^{7+2} )^3}{(a^{5+3} )^2}= \frac{(a^9)^3}{(a^8)^2}= \frac{ a^ {27}}{ a^{16} } =a^{27-16}=a^{11}[/tex]
[tex]stosujemy\ wzory :\\\\a^n*a^m=a^{n+m}\\\\a^n:a^m=a^{n-m} \\\\(a^n)^m=a^{n*m}[/tex]
[tex]7)\\\\ \left [(a^3)^5:(a^2*a^8)^2 * a^7 \right ] ^5:a^6 =\left [ a^{15} :(a^{2+8} )^2 * a^7 \right ] ^5:a^6=\\\\=\left [ a^{15} :(a^{10} )^2 * a^7 \right ] ^5:a^6 =\left [ a^{15} : a^{20} * a^7 \right ] ^5:a^6 =\left [ a^{15-20+7} \right ] ^5:a^6 = \\\\=(a^{2}) ^5:a^6 = a^{10} :a^6 =a^{10-6}=a^4 \\\\\\a=1\frac{2}{3}=\frac{5}{3}\\\\a^4=(\frac{5}{3})^4=\frac{625}{256}=2\frac{113}{256}[/tex]
