First, let's simplify the expression (3a^-4 / 2b^-3)^-2:

(3a^-4 / 2b^-3)^-2 = (3^2a^-4 / 2^2b^-3)^-1
= (9 / 4 a^-4 / b^-3)^-1
= (9 / 4 a^-4 / b^-3)^-1
= 4 / 9 * b^3 / a^4

Now let's multiply the simplified expression by 10a^7 b^3:

(4 / 9 b^3 / a^4) 10a^7 b^3
= (40 / 9 * b^6 / a^4)
= 40b^6 / 9a^4

Therefore, the final simplified expression is 40b^6 / 9a^4.