If m and n are whole numbers with m^n = 121, evaluate (m − 1)^n + 1.

Given data

• m^n = 121.

Concept / Approach

• Prime factorize 121 to find integer m and n.

Step-by-step calculation

121 = 11^2 ⇒ m = 11, n = 2 (whole numbers).(m − 1)^n + 1 = (11 − 1)^2 + 1 = 10^2 + 1 = 101.

Verification

No other whole-number power representations exist for 121.

Common pitfalls

• Interpreting mn as m×n rather than m^n; that would not give a unique value.

Final Answer

101.