[tex]f) \ 7\cdot5^{6}-2\cdot25^{3} =7\cdot5^{6}-2\cdot(5^{2})^{3} =7\cdot5^{6}-2\cdot5^{6} = 5^{6}(7-2) = 5^{6}\cdot5 = 5^{7}[/tex]
[tex]g) \ \frac{(2^{3})^{2}\cdot3^{3}+15\cdot3^{2}-5\cdot27}{3^{3}\cdot2} =\frac{2^{6}\cdot3^{3}+5\cdot3\cdot3^{2}-5\cdot3^{3}}{3^{3}\cdot2}=\frac{2^{6}\cdot3^{3}+5\cdot3^{3}-5\cdot3^{3}}{3^{3}\cdot2}=\frac{2^{6}\cdot3^{3}}{3^{3}\cdot2}=\frac{2^{6}}{2} = 2^{5}[/tex]
