If a and b are whole numbers such that ab = 121, then find the value of (a –…

Concept: Laws of exponents — to find whole numbers a and b satisfying ab = N, express N as (base)exponent; matching the base and exponent gives a and b directly, which can then be substituted into any related expression.

1. 121 can be written as 112, so ab = 112 gives a = 11 and b = 2. (The trivial reading 121 = 1211, i.e. a = 121, b = 1, also fits ab = 121, but it gives (a – 1)b + 1 = 1202, a value not present among the offered options — so the non-trivial pair a = 11, b = 2 is the one intended here.)

2. Substitute into (a – 1)b + 1: (11 – 1)2 + 1 = 103.

3. Evaluate: 103 = 1000.

Cross-check: squaring 11 gives 112 = 121, confirming a = 11 and b = 2; and 103 is exactly the value option (103) represents, confirming the match.