a)
[tex]3^{101}: 9^{50}= 3^{101}: 3^{2*50}= 3^{101}: 3^{100}= 3^{1} =3[/tex]
b)
[tex](3^{57} :9^{25}* 3^{10} ):3^{15}= (3^{57} :3^{2*25}* 3^{10} ):3^{15}= (3^{57} :3^{50}* 3^{10} ):3^{15}= (3^{7} * 3^{10} ):3^{15}= 3^{17} :3^{15}= 3^{2} =9[/tex]
c)
[tex]2*4*2^{43} -2^{46} +(9^{74} :3^{43}-(3^{15}) ^{6} )^{0} =2*2^{2} *2^{43} -2^{46} +1 =\\2^{46} -2^{46} +1=0+1=1[/tex]