Solving a digit arrangement puzzle to maximize a given product

Convert the entire expression into a common base of 2 to simplify the terms: 32 = 2^5 \implies 32^5 = (2^5)^5 = 2^25.

The full expression becomes: 2^25 + 2^27. Factor out the lowest common exponent component 2^25: 2^25(1 + 2²) = 2^25(1 + 4) = 2^25 × 5.

Now look at the simplified product: 2^25 × 5. This product contains a multiple of 2 and a multiple of 5. Any number that is a multiple of both 2 and 5 must be divisible by ⟨MATH⟩2 × 5 = 10⟨/MATH⟩.

Answer: (c).