Question:

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

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Familiarity with squares and cubes of numbers up to 20 helps quickly identify relationships like \(14^2 = 196\) and \(11^3 = 1331\).
Updated On: May 9, 2026
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The Correct Option is D

Solution and Explanation



Step 1: Understanding the Question:

We are given an equation \(m^n = 196\) where \(m\) and \(n\) are whole numbers.
We need to find the possible values for \(m\) and \(n\) and then evaluate the given expression.


Step 2: Key Formula or Approach:

Express the number \(196\) as a power of a whole number to find matching values for the base \(m\) and exponent \(n\).


Step 3: Detailed Explanation:

We know that \(196\) is a perfect square.
\[ 196 = 14^2 \] Comparing this with \(m^n\), we get \(m = 14\) and \(n = 2\).
(Note: Another possibility is \(196^1\), which gives \(m = 196, n = 1\). However, since test questions typically aim for the simplest non-trivial base, we proceed with \(m=14, n=2\)).
We need to find the value of \((m - 3)^{n + 1}\).
Substitute the values of \(m\) and \(n\): \[ (14 - 3)^{2 + 1} \] \[ = (11)^3 \] \[ = 11 \times 11 \times 11 = 1331 \] This matches option (D).


Step 4: Final Answer:

The value of the expression is \(1331\).
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