a) [tex]2 ^{17} *2 ^{21} =2^{17+21}=2^{38}[/tex]
b)[tex]3 ^{45} *3 ^{87}*3 ^{55} =3^{45+87+55}=3^{187}[/tex]
c)[tex]7 ^{19} *7 ^{83} *7=7^{19+83+1}=7^{103}[/tex]
d)[tex]2 ^{47} :2 ^{39} =2^{47-39}=2^{8}[/tex]
e)[tex]5 ^{108} :5 ^{72} =5^{108-72}=5^{36}[/tex]
g)[tex](10 ^{12}) ^{15} =5^{12*15}=5^{180}[/tex]
h)[tex](2 ^{17}) ^{8}*2 ^{31} =2^{17*8}*2 ^{31}=2^{136}*2 ^{31}=2 ^{136+31}=2 ^{167}[/tex]
i)[tex]3 ^{108}:(3 ^{15})^{6} =3^{108} :3^{15*6} = 3^{108}:3^{90}=3^{108-90}=3^{18}[/tex]
j)[tex](3^{7} * 5^{12} ) ^{2}= (3^{7})^{2} *( 5^{12} ) ^{2}=3^{7*2}*5^{12*2}=3^{14}*5^{24}[/tex]