a: \(=2^7\)
b: \(=5^{12}\)
c: \(=3^{2+4+6}=3^{12}\)
d: \(=a^{2+3+5}=a^{10}\)
e: \(=3^3\cdot3^6\cdot3^4=3^{13}\)
f: \(=10^2\cdot10^3\cdot10^4=10^9\)
\(a,2^3\cdot2^4=2^{3+4}=2^7\\ ~\\ b,5^5\cdot5^7=5^{5+7}=5^{12}\\ ~\\ c,3^2\cdot3^4\cdot3^6=3^{2+4+6}=3^{12}\\ ~\\ d,a^2\cdot a^3\cdot a^5=a^{2+3+5}=a^{10}\\ ~\\ e,3^3\cdot9^3\cdot81=3^3\cdot\left(3^2\right)^3\cdot3^4=3^3\cdot3^6\cdot3^4=3^{3+6+4}=3^{13}\\ ~\\ f,100\cdot1000\cdot100^2=100^3\cdot1000\)