a.$(\frac{1}{5})^{10}$.$25^{5}$
= $(\frac{1}{5})^{10}$.$(5^{2})^{5}$
= $(\frac{1}{5})^{10}$.$5^{10}$
= $(\frac{1}{5}.5)^{10}$
= $1^{10}$
= 1
b. $(\frac{1}{2})^{9}$.$8^{4}$
= $(\frac{1}{2})^{9}$.$(2^{3})^{4}$
= $[(\frac{1}{2})^{3}]^{3}$. $(2^{3})^{4}$
= $[(\frac{1}{2}.2)^{3})]^{12}$
= $(1^{3})^{12}$
= $1^{12}$ = 1
c. $(0,25)^{10}$.$8^{6}$
= $[(0,5)^{2}]^{2}$.$(2^{3})^{6}$
= $[(0,5)^{2}]^{2}$.$2^{18}$
= $[(\frac{1}{2})^{2}]^{2}$.$(2^{2})^{9}$
= $[(\frac{1}{2}.2)^{2})]^{18}$
= $(1^{2})^{18}$
= $1^{18}$ = 1
d. $2^{2020}$ : $2^{2018}$
= $2^{2020 - 2018}$
= $2^{2}$ = 4
