a)
[tex]\it = \dfrac{3^{22}(3^2+3-2)}{9^{11}(1+9)} = \dfrac{(3^2)^{11}\cdot10}{9^{11}\cdot10} =\dfrac{9^{11}}{9^{11}} = 1[/tex]
c)
[tex]\it \dfrac{5^{30}}{3^{45}} = \dfrac{(5^2)^{15}}{(3^3)^{15}}=\left(\dfrac{25}{27}\right)^{15}[/tex]
d)
[tex]\it \dfrac{3^{39}+3^{38}}{2^{59}} =\dfrac{3^{38}(3+1)}{2^{57}\cdot 2^2} = \dfrac{3^{38}\cdot4}{2^{57}\cdot 4} = \dfrac{3^{38}}{2^{57}} = \dfrac{(3^2)^{19}}{(2^3)^{19}} = \left(\dfrac{9}{8}\right)^{19} [/tex]
