Final answer:
To determine the value of k that makes the given equation (5a²b³)(6a⁴b) = 30a⁶b⁴ true, we observe that by multiplying the coefficients and adding exponents of like bases, the equation is inherently balanced without needing a value for k.
Step-by-step explanation:
To find the value of k that makes the equation true, we need to multiply the two expressions by applying the exponent rules. The given equation is (5a²b³)(6a⁴b) = 30a⁶b⁴. First, multiply the coefficients (numerical values) and then add the exponents of the like variables. Recall that when multiplying powers with the same base, you add the exponents.
Multiplying the coefficients: 5 * 6 = 30
Adding the exponents of a: 2 (from a²) + 4 (from a⁴) = 6
Adding the exponents of b: 3 (from b³) + 1 (from b¹) = 4
So the equation simplifies to 30a⁶b⁴, which matches the right side of the original equation. Hence, k does not need a value in this case because the equation is already balanced as it stands.