Final answer:
There is no value of k that makes the equation true.
Step-by-step explanation:
To find the value of k that makes the equation true, we need to compare the exponents of a and b on both sides of the equation.
On the left side of the equation, the exponent of a is 2 (5a²b³) and the exponent of b is 3+k (6aᵏ(b)).
On the right side of the equation, the exponent of a is 6 (30a⁶(b⁴)) and the exponent of b is 4.
Since the exponents of a must be equal on both sides of the equation, we have the equation 2 = 6, which is not true for any value of k.
Therefore, there is no value of k that makes the equation true. The correct answer is none of the above.