To simplify this expression step by step, we will first expand the exponents and then simplify the resulting expression.

(-7x^2/3y^4)^-3 * (9y^2/49x^4)^-2

First, expand the exponents and distribute the negative exponents:

((-7)^-3 x^(-2 -3) y^(4 -3)) ((9)^-2 y^(2 -2) x^(-4 -2)) / (3^-3 y^(-4 -3) 49^-2 x^(4 -2))

Now simplify the exponents:

((-1/343) x^6 y^-12) (1/81 y^-4 x^8) / (1/27 y^-12 1/2401 x^8)
(-1/343 x^6 y^-12) (1/81 y^-4 x^8) / (1/27 y^-12 1/2401 x^8)
(-1/343 x^6 y^-12) (1/81 y^-4 x^8) / (1/27 y^-12 1/2401 x^8)
(-1/343 1/81 x^6 y^-12 y^-4 x^8) / (1/27 1/2401 y^-12 x^8)
(-1/27783 x^14 y^-16) / (1/64827 y^-12 x^8)
(-1/27783 64827/27783 x^14 y^4 x^8) / y^12
(-64827/27783 x^22) / y^12
-2.33 x^22 / y^12

Therefore, the simplified expression is -2.33x^22 / y^12.