[tex]a) \ \frac{(2^{2})^{3}}{4\cdot2^{3}}} = \frac{2^{2\cdot3}}{2^{2}\cdot2^{3}} =\frac{2^{6}}{2^{2+3}} = \frac{2^{6}}{2^{5}} = 2^{6-5} = 2^{1} = 2\\\\b) \ (2^{2}+3^{2})^{2} = (4+9)^{2} = 13^{2} = 13\cdot13 = 169\\\\c) \ 2\cdot5^{3}+3\cdot5^{3} = 5^{3}\cdot(2+3) = 5^{3}\cdot5 = 5^{3+1} = 5^{4} = 625\\\\d) \ \frac{6^{5}}{3^{3}\cdot2^{3}} = \frac{6^{5}}{(2\cdot3)^{3}} = \frac{6^{5}}{6^{3}} = 6^{5-3} = 6^{2} = 36[/tex]
