Rewrite to powers of 2 and compare exponents: If 16 × 8^(n+2) = 2^m, find m in terms of n.

Introduction / Context:Here we convert mixed bases (16 and 8) to a single base 2, then equate exponents. This is a routine indices exercise reinforcing base conversion and exponent addition.

Given Data / Assumptions:

• 16 × 8^(n+2) = 2^m
• 16 = 2^4 and 8 = 2^3

Concept / Approach:Rewrite everything as powers of 2. Add exponents on the left (since same base multiplied), then set the combined exponent equal to m.

Step-by-Step Solution:16 = 2^48^(n+2) = (2^3)^(n+2) = 2^(3(n+2)) = 2^(3n + 6)LHS = 2^4 × 2^(3n + 6) = 2^(4 + 3n + 6) = 2^(3n + 10)Thus 2^m = 2^(3n + 10) ⇒ m = 3n + 10

Verification / Alternative check:Plug n = 0: LHS = 16 × 8^2 = 16 × 64 = 1024 = 2^10 ⇒ m = 10, consistent with 3(0)+10.

Why Other Options Are Wrong:They reflect incorrect coefficient arithmetic (e.g., forgetting the +6 or mis-scaling the 3 on n).

Common Pitfalls:Expanding 3(n+2) incorrectly or missing the 2^4 factor from 16.

Final Answer:3n + 10