what is the sum of the x-exponent of the vectors 4m south and 4m 60degree north of east ? *e stands for exponent*

I think the questioner wants to know this:

The sum of the "x" components of a 270°  vector with a length of 4 and a 60° vector with a length of 4.

So, for the 270° vector we have, < 0. 4 >  and for the 60° vector we have < 2 ,  2√3 > .

So, as Melody has said, the sum of the "x" components is just  2.

Do you mean the x-component?  If so, the x-component of a vector pointing south is zero, and the x-component of a vector of length 4m pointing in the direction 60° north of east is 4cos(60°)m or 2m (since cos(60°) is 1/2).

However, I might have misunderstood your question!

I am adding the vectors end to end.

$$\\sin30^0=\dfrac{x}{4}\\\\
x=4sin30^0\\\\
x=2$$

The sum of the x components is 0+2=2