a)
[tex]( {2}^{10} \times {2}^{5} \times {7}^{4} {)}^{2} = ( {2}^{15} \times {7}^{4} {)}^{2} = {2}^{30} \times {7}^{8} [/tex]
[tex]m = 30 \\ \\ n = 8[/tex]
b)
[tex] \frac{( {3}^{4} \times {5}^{7} {)}^{3} }{ {5}^{9} } = \frac{ {3}^{12} \times {5}^{21} }{ {5}^{9} } = {3}^{12} \times {5}^{12} [/tex]
[tex]m = 12 \\ \\ n = 12[/tex]
c)
[tex]4 \times ( \frac{ {2}^{3} }{ {3}^{4} } {)}^{10} = {2}^{2} \times \frac{ {2}^{30} }{ {3}^{40} } = \frac{ {2}^{32} }{ {3}^{40} } [/tex]
[tex]m = 32 \\ \\ n = 40[/tex]
d)
[tex]( \frac{ {7}^{3} }{ {5}^{2} } {)}^{3} \times ( \frac{ {5}^{3} }{ {7}^{5} } {)}^{4} = \frac{ {7}^{9} }{ {5}^{6} } \times \frac{ {5}^{12} }{ {7}^{20} } = {7}^{9} \times \frac{ {5}^{6} }{ {7}^{20} } = \frac{ {5}^{6} }{ {7}^{11} } [/tex]
[tex]m = 6 \\ \\ n = 11[/tex]
