First, simplify the expression (7x^2)^3:
(7x^2)^3 = 7^3 \cdot (x^2)^3 = 343x^6
Then, combine it with x^{-4} using the property of exponents a^m \cdot a^n = a^{m+n} :
343x^6 \cdot x^{-4} = 343x^{6-4} = 343x^2
So the final simplified expression is:
343x^2