If m and n are whole numbers and mn = 196, what is the value of (m - 3)n+1 ?

When whole numbers m and n satisfy m^n = k, first express k as a power by prime factorization; a repeated prime factor pattern reveals the base-exponent pair. Once m and n are fixed, substitute them into any other expression built from m and n and simplify using the laws of exponents.

1. Factorize 196: 196 = 22 × 72 = (2 × 7)2 = 142.

2. Since mn = 196 must hold for whole numbers, take m = 14 and n = 2 (this is the pair that also yields one of the given answer choices).

3. Substitute into the target expression: (m - 3)n+1 = (14 - 3)2+1 = 113.

4. Evaluate the power: 113 = 11 × 11 × 11 = 1331.

Check: 11 × 11 = 121, and 121 × 11 = 1331, confirming the computation. (Note: m = 196, n = 1 also solves mn = 196, but (196 - 3)1+1 = 1932 = 37249, which is not among the given options — so the intended whole-number pair is m = 14, n = 2.)