Final answer:
The equivalent algebraic expression to the given algorithm is option 1: 8K3 + 24K2 + 72K + 216, which takes into account the cubing of the entire expression (K + 3) and multiplying it by 8.
Step-by-step explanation:
The student's question involves determining the algebraic expression equivalent to a given algorithm. The key here is understanding how exponents operate when numbers or variables are raised to powers, especially when they are enclosed in parentheses. The rule is that when you raise a power to another power, you multiply the exponents. This is seen in the expression: (K3)4 = K3*4 = K12, which simplifies by multiplying the two exponents. Similarly, cubing an exponential expression, (27x3)(4x2), involves raising each part of the expression to the cube, thus affecting both the numerical coefficient and its exponents.
Using this principle, the expression corresponding to the algorithm would involve cubing not just the variable but the entire expression within the parentheses, as seen in option 4: (8(K + 3)3). This is because cubing '(K + 3)' not only cubes the variable K to K3 but also accounts for the cubed products of the sum of K and 3. It would result in an expansion where the coefficient 8 affects each term in the binomial expansion of (K + 3)3, leading to the algebraic expression 8K3 + 24K2 + 72K + 216, making option 1 the correct answer.