The value of k that would satisfy the expression is "1". How to get this, the solution is shown below:
xky4 (2x3 + 7x2y4) = 2x4y4 + 7x3y8
Distribute xy4 to the parentheses such as:
k (2x4y4 + 7x3y8) = 2x4y4 + 7x3y8
Divide both sides by 2x4y4 + 7x3y8 such as shown below:
k = (2x4y4 + 7x3y8) / (2x4y4 + 7x3y8)
k=1
The answer is "1".