a)
[tex]128 \times {5}^{7} = {2}^{7} \times {5}^{7} = {(2 \times 5)}^{7} = {10}^{7} = 10 \: 000 \: 000[/tex]
b)
[tex] {25}^{3} \times 64 = { ({5}^{2}) }^{3} \times {2}^{6} = {5}^{6} \times {2}^{6} = {(5 \times 2)}^{6} = {10}^{6} = 1 \: 000 \: 000[/tex]
c)
[tex] \frac{ {10}^{4} }{ {5}^{7} } \times 125 = \frac{ {(5 \times 2)}^{4} }{ {5}^{7} } \times {5}^{3} = \frac{ {5}^{4} \times {2}^{4} }{ {5}^{7} } \times {5}^{3} = \frac{ {5}^{4} }{ {5}^{7} } \times {2}^{4} \times {5}^{3} = {5}^{ - 3} \times {2}^{4} \times {5}^{3} = {2}^{4} \times {5}^{0} = 16 \times 1 = 16[/tex]
d)
[tex] {( - 3)}^{5} = - 243[/tex]
