\(A=\dfrac{4\cdot5^{10}\cdot5^{10}}{75^{10}}=\dfrac{4\cdot5^{20}}{\left(3\cdot25\right)^{10}}=\dfrac{4\cdot5^{20}}{3^{10}\cdot25^{10}}=\dfrac{4\cdot5^{20}}{3^{10}\cdot\left(5^2\right)^{10}}=\dfrac{4\cdot5^{20}}{3^{10}\cdot5^{20}}=\dfrac{4}{3^{10}}\)
\(B=\dfrac{\left(0.8\right)^5}{\left(0.4\right)^6}=\dfrac{\left(\dfrac{4}{5}\right)^5}{\left(\dfrac{2}{5}\right)^6}=\dfrac{\left(2\cdot\dfrac{2}{5}\right)^5}{\left(\dfrac{2}{5}\right)^6}=\dfrac{2^5\cdot\left(\dfrac{2}{5}\right)^5}{\left(\dfrac{2}{5}\right)^5\cdot\dfrac{2}{5}}=\dfrac{2^5}{\dfrac{2}{5}}=2^5\cdot\dfrac{5}{2}=\dfrac{32\cdot5}{2}=80\)
\(C=\dfrac{2^{15}\cdot9^4}{6^6\cdot8^3}=\dfrac{2^{15}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^6\cdot\left(2^3\right)^3}=\dfrac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=\dfrac{2^{15}\cdot3^8}{2^6\cdot2^9}=\dfrac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=\dfrac{3^8}{3^6}=3^2=9\)
\(D=\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{^{20}}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=\dfrac{2^{20}}{2^{12}}=2^8=226\)
