[tex]a)\\\\ \left [ (ab)^3 \right ]^4:\left [ (ab)^3 \right ]^3=(ab)^3\\\\ L=\left [ (ab)^3 \right ]^4:\left [ (ab)^3 \right ]^3=\left [ (ab)^3 \right ]^{4-3}=(ab)^3\\\\P=(ab)^3\\\\L=P\\\\prawda[/tex]
[tex]b)\\\\ \left [ (ab^3)^2 \right ]^ 3* (a^6)^2 = \left [ (ab^5)^2*(a^2) \right ]^4*(b^4)^2\\\\ L= \left [ (ab^3)^2 \right ]^ 3* (a^6)^2 =\left [ (ab^3)^{2*3} \right ] * a^{6*2 } =\left [ (ab^3)^{6} \right ] * a^{12} =a^6*b^{3*6}*a^{12} =\\\\=a^6*b^{18}*a^{12}=a^{6+12}*b^{18}=a^{18}b^{18}\\\\P=\left [ (ab^5)^2*(a^2) \right ]^4*(b^4)^2=\left [ a^2*b^{5 *2}* a^2 \right ]^4* b^{4*2}=\\\\\left [ a^2*b^{10}* a^2 \right ]^4* b^{8} =a^{2*4}*b^{10*4}* a^{2*4} *b^8=a^{8}*b^{40}* a^{8} *b^8=a^{8+8}*b^{40+8}=\\\\=a^{16}*b^{48}\\\\L\neq P\\\\Falsz[/tex]
[tex]c)\\\\ (y^3)^2*(x^2y)^6 =((xy)^2)^4*(x^2)^2 *y^4\\\\L=(y^3)^2*(x^2y)^6 = y^{3 *2}* x^{2*6}*y ^6 = y^{6}* x^{12}*y ^6 =x^{12}*y^{6+6} =x^{12}*y^{12}=(xy)^{12} \\\\P=((xy)^2)^4*(x^2)^2 *y^4= (xy)^{2 *4} x^{2 *2} *y^4 = (xy)^{8} x^{4} *y^4 = \\\\= (xy)^{8} ( xy)^{4}=(xy)^{8+4}=(xy)^{12}\\\\L=P\\\\Prawda[/tex]
[tex]d)\\\\ \left [ (x^2)^3*x \right ]^2*( y^{16}: y^2=) \left [(y^2)^3*y^3 \right ]^2*(x^{16}:x^2)\\\\L=\left [ (x^2)^3*x \right ]^2*( y^{16}: y^2)=\left [ x^{2*3 }*x \right ]^2* y^{16-2}=\\\\= \left [ x^{6 }*x \right ]^2* y^{14}= \left [ x^{6+1 } \right ]^2* y^{14}= \left [ x^{7 } \right ]^2* y^{14}= x^{7*2 } * y^{14}= x^{14}*y^{14}\\\\L=\left [(y^2)^3*y^3 \right ]^2*(x^{16}:x^2)=\left [ y^{2*3 }*y^3 \right ]^2* x^{16-2}=\left [ y^{6 }*y^3 \right ]^2* x^{14} =\\\\=\left [ y^{6+3 } \right ]^2* x^{14}=\left [ y^{9 } \right ]^2* x^{14}= y^{9*2 }* x^{14} =x^{14}*y^{18}\\\\L\neq P\\\\Falsz[/tex]
