(a)
\frac{2\cdot 3^{20}-5\cdot 3^{19}}{9^9}=\\\\=\frac{2\cdot 3^{2}\cdot 3^{18}-5\cdot 3^1\cdot 3^{18}}{(3^2)^9}\\\\=\frac{18\cdot 3^{18}-15\cdot 3^{18}}{3^{18}}\\\\ =\frac{\not3^{18}(18-15)}{\not3^{18}}=\frac{3}{1}=3
(d)
\frac{(3^{15}+3^{13}) \cdot 2^9}{(3^{14}+3^{12})\cdot 1024}=
=\frac{(3^{12} \cdot 3^3+3^{12}\cdot 3^1) \cdot 2^9}{(3^{12}\cdot 3^2+3^{12})\cdot 2^{10}}
=\frac{\not3^{12}(3^3+3)\cdot \not2^9}{\not3^{12}(9+1)\cdot \not2^9 \cdot 2^1}=\frac{27+3}{10\cdot 2}=\frac{30}{20}=\frac{3}{2}