[tex]a) {3}^{15} : {27}^{4} = {3}^{15} : {3}^{12} = {3}^{15 - 12} = {3}^{3} = 27 [/tex]
[tex]b) {4}^{10} : {16}^{4} = {4}^{10} : {4}^{8} = {4}^{10 - 8} = {4}^{2} = 16 [/tex]
[tex]c) {2}^{105} : {4}^{51} = {2}^{105} : {2}^{102} = {2}^{105 - 102} = {2}^{3} = 8 [/tex]
[tex]d) {4}^{3} \times {8}^{2} : {16}^{3} = {2}^{6} \times {2}^{6} : {4}^{6} = {2}^{6} \times {2}^{6} : {2}^{12} = {2}^{6} \times {2}^{6} : {2}^{ - 12} = {2}^{6 + 6 - 12} = {2}^{0} = 1 [/tex]
[tex]e) {16}^{15} : {32}^{12} = {2}^{60} : {2}^{60} = 1 [/tex]
[tex]f) {25}^{30} : {125}^{20} = {5}^{60} : {5}^{60} = 1[/tex]
