a: \(\dfrac{18^5}{4^5\cdot9^5}=\left(\dfrac{18}{36}\right)^5=\left(\dfrac{1}{2}\right)^5=\dfrac{1}{32}\)
b: \(\dfrac{16^2}{3^2\cdot4^4}=\dfrac{2^8}{3^2\cdot2^8}=\dfrac{1}{3^2}=\dfrac{1}{9}\)
c: \(\dfrac{8^5\cdot12^4}{4^3\cdot8^6}=\dfrac{2^{15}\cdot2^8\cdot3^4}{2^6\cdot2^{18}}=\dfrac{1}{2}\cdot3^4=\dfrac{81}{2}\)
d: \(\dfrac{8^2+3\cdot4^2+128}{2^5}=\dfrac{2^6+3\cdot2^4+2^7}{2^5}\)
\(=\dfrac{2^4\left(2^2+3+2^3\right)}{2^5}=\dfrac{1}{2}\cdot\dfrac{4+3+8}{1}=\dfrac{15}{2}\)
e: \(\left(-1\right)^{20}+1,69\left(3,5-2,2\right)^2-\left(-1,69\right)^2\)
\(=1+1,69\cdot1,3^2-1,69^2=1+1,3^4-1,3^4=1\)
f: \(\dfrac{4^{19}+8^7}{256^4+32^3}=\dfrac{2^{38}+2^{21}}{2^{32}+2^{15}}=\dfrac{2^{21}\left(2^{17}+1\right)}{2^{15}\left(2^{17}+1\right)}=2^6=64\)
