Which expression is equivalent to (a^4bc^6)^3?

Using the exponent rule for raising a power to a power, we have \[(a^4bc^6)^3=a^{(4)(3)}b^{(1)(3)}c^{(6)(3)}=a^{12}b^3c^{18}=\boxed{a^{12}b^3c^{18}}.\]