a: \(4^8\cdot2^{20}=\left(2^2\right)^8\cdot2^{20}=2^{16}\cdot2^{20}=2^{16+20}=2^{36}\)
\(9^{12}\cdot27^5\cdot81^4=\left(3^2\right)^{12}\cdot\left(3^3\right)^5\cdot\left(3^4\right)^4\)
\(=3^{24}\cdot3^{15}\cdot3^{16}=3^{24+15+16}=3^{55}\)
\(64^3\cdot4^5\cdot16^2=\left(4^3\right)^3\cdot4^5\cdot\left(4^2\right)^2=4^9\cdot4^5\cdot4^4=4^{9+5+4}=4^{18}\)
b: \(25^{20}\cdot125^4=\left(5^2\right)^{20}\cdot\left(5^3\right)^4=5^{40}\cdot5^{12}=5^{52}\)
\(x^7\cdot x^4\cdot x^3=x^{7+4+3}=x^{14}\)
\(3^6\cdot4^6=\left(3\cdot4\right)^6=12^6\)
c: \(8^4\cdot2^3\cdot16^2=\left(2^3\right)^4\cdot2^3\cdot\left(2^4\right)^2\)
\(=2^{12}\cdot2^3\cdot2^8=2^{23}\)
\(y\cdot y^7=y^{1+7}=y^8\)
\(2^3\cdot2^2\cdot8^3=2^5\cdot\left(2^3\right)^3=2^5\cdot2^9=2^{5+9}=2^{14}\)
