Final answer:
The integer value of k that satisfies the equation 3³ + 3³ + 3³ = 243 × 3ᵏ is k = 2.
Step-by-step explanation:
To find the value of k, we need to simplify the equation and compare the coefficients. We have 3³ + 3³ + 3³ = 243 × 3ᵏ. When we simplify the left side of the equation, we get 27 + 27 + 27 = 81. So the equation becomes 81 = 243 × 3ᵏ. Now, we can divide both sides of the equation by 243 to isolate 3ᵏ. 81 ÷ 243 = 3ᵏ. This simplifies to 1/3 = 3ᵏ-3, or 3 = 3ᵏ-2. Since both sides of the equation are equal, we can conclude that the value of k is 2.