4a) [tex]250^{4}=250^{2+2} =250^{2} [/tex]×[tex] 250^{2}= (250^{2})^{2} [/tex] -patrat perfect
b)[tex] 5^{206}=5^{103+103}= 5^{103} [/tex]×[tex] 5^{103}= (5^{103})^{2} [/tex]
[tex] 7.a) [6^{100}*2^{50}+(3^{17}) ^{10}+ 25^{37}]: [2^{150}*3^{100}+(3^{10}) ^{17} +5^{74}]= \\ \\ \\ =[(2*3) ^{100}* 2^{50} +3^{170} +5^{2*37)} ]:[2^{150}*3^{100}+3^{(10*17)}} + 5^{74}] \\ \\ =[2 ^{(100+50)} *3^{100}+ 3^{170} +5^{74} ]:[2^{150}*3^{100}+3^{170}++5^{74}] \\ \\ =[2^{150}*3^{100}+3^{170}++5^{74}] :[2^{150}*3^{100}+3^{170}++5^{74}] \\ \\ =1[/tex]
