(-7a^4bc^3)(5ab^4c^2)
The easiest way is to look at them separately by like variables and constants.
(-7 * 5) (a^4 * a) (b * b^4) c^3 * c^2)
-35 a^5 b^5 c*5
(16 t^4)/(8t) again 16/8 = 2 t^4 / t = t^3 so.... 2t^3
(x^6y^14)/(x^4y^9) separate again (x^6/x^4)= x^2; (y^14/y^9) = y^5 so....x^2y^5
(3^4x^4)/(3x^2) = (3^4/3^1) = 3^3 = 27; (x^4/x^2) = x^2; answer is 27x^2