Question

w^3 + 343/ w^11 - 49W^9 (times) w^12 -14w^11 +49w^10/ w^2-7w +49

Answer 1

w^3 + 343 = w^3 + 7^3 = (w+7)(w^2-7w+49)

w^11 - 49w^9 = w^9 (w^2-49) = w^9 (w-7)(w+7)
w^12 -14w^11 +49w^10 = w^10 (w^2-14w+49) = w^10 (w-7)^2
w^2-7w+49 we saw above

so, see what you can make cancel out with all that!