[tex]3a.(5^{4} )^{6}=5^{4*6}=5^{24} ; b)(7^{8} )^{3}= 7^{8*3}=7^{24} ;e)(3^{2} )^{3})^{4} )=3^{2*3*4}= 3^{24 \\ \\[/tex]
[tex]f) 8^{5})^{3^{6} }=8^{5*3*6}=8^{90} \\ \\ 4.a) (2*7)^{14}=2^{14}*7^{14} \\ \\ b) (3*5)^{7}=3^{7}*5^{7} \\ \\ e)= (3*8*5)^{4}; f)=(2*7)^{15}[/tex]
[tex]5.a)12^{24}:3^{24}=3^{24} *4^{24}: 3^{24} =4^{24}\\ \\b)125^{45}:5^{45}=5^{3*45}:5^{45} =5^{3} \\ \\ e)(27:3) ^{21} = (3^{3} :3) ^{21} =3 ^{2*21}=3x^{42} \\ \\ f)(24:4)^{31} =(6*4:4) ^{31} =6^{31} [/tex]
[tex]6.a. (2^{3})^{8} :4^{11} = 2^{24}:2^{22} =2^{2}=4 \\ b)3^{7})^{4}:9^{13}=3^{28}:3 ^{2*13}=3^{2}=9 \\ e) 125^{12}:25^{17} =5^{3*12} :5^{2*17} =5^{36-34} =5 ^{2} =25; \\ f)81^{36} :27^{48} = 3^{4*36}:3^{3*48}=1 [/tex]
[tex]7.a.2^{24}-2^{24}=0; \\ b)3^{7})^{4}:3^{26}=3^{2}=9; \\ d)5^{8})^{7}:5 ^{35}*5=5^{56}:5^{36}=5^{20} \\ g)(7^{13})^{2}:7^{42})^{4} =7^{169}:7 x^{168}=7 \\ e)7^{42}:7 ^{40}= 7^{2}=49 \\ h)(2^{7}) ^{2}:(2^{8}) =2^{49}:2 ^{48}=2 [/tex]
