Answer:
k=1
Step-by-step explanation:
Let us simplify the left hand side of the given expression .
[tex]x^k \times y^4 (2x^3+7x^2\times y^4)=2x^k^+^3 \times y^4 +7x^k^+^2 \times y^8[/tex]
The exponent of the like terms gets added on multiplication like
[tex]a^m \times a^n = a^m^+^n[/tex]
Now we compare the left hand side expression with the right hand side.
Since they should be equal to each other , so comparing their exponents and equating them.
Exponents of [tex]x[/tex] should be same on either side.
Therefore, [tex]k+3 = 4\\gives\\k=1[/tex]
Similarly on comparing the other 'x' exponent
[tex]k+2 = 3\\gives\\k=1[/tex]
Thus [tex]k=1[/tex] is the required answer.
