Explicação passo-a-passo:

A)

[tex]144 | 2 \\ 72 | 2 \\ 36 | 2 \\ 18 |2 \\ 9 | 3 \\ 3 | 3 \\ 1 \\ 144 = {2}^{4} \times {3}^{2}[/tex]

B)

[tex]105 | 3 \\ 35 | 5 \\ 7 | 7 \\ 1 \\ 105 = 3 \times 5 \times 7[/tex]

C)

[tex]180 | 2 \\ 90 | 2 \\ 45 | 3 \\ 15 | 5 \\ 3 | 3 \\ 1 \\ 180 = {2}^{2} \times {3}^{2} \times 5[/tex]

d)

[tex]500 | 2 \\ 250 | 2 \\ 125 | 5 \\ 25 | 5 \\ 5 | 5 \\ 1 \\ 500 = {2}^{2} \times {5}^{3} [/tex]

E)

[tex]256 | 2 \\ 128 | 2 \\ 64 | 2 \\ 32 | 2 \\ 16 | 2 \\ 8 | 2 \\ 4 | 2 \\ 2 | 2 \\ 1 \\ 256 = {2}^{8} [/tex]

F)

[tex]340 | 2 \\ 170 | 2 \\ 85 | 5 \\ 17 | 17 \\ 1 \\ 340 = {2}^{2} \times 5 \times 17[/tex]

G)

[tex]507 | 3 \\ 169 | 13 \\ 13 | 13 \\ 1 \\ 507 = {13}^{2} \times 3[/tex]