It's the right answer right

x^1/3 times x^1/4 equals x^5/12, is that right?

No! its suppose to be x^7/12
i.e x^(1/3 + 1/4)
LCM = 12, 3 into 12 is 4 and 4 times 1 is 4 also 4 into 12 is 3 and 3 times 1 is 3,
x^(4 + 3)/12 = x^7/12.

No !

You have to add the powers (indices).

1/3 + 1/4 = 4/12 +3/12 = 7/12

no!
x^a x x^b = x^a+b
x^a / x^b = x^a-b
hence x^1/3 + x^1/4 = x^(1/3+1/4)= x^7/12

Wrong

x^(1/3) * x(1/4) = x^(4/12) * x^(3/12) = x^(7/12)