Electrode potential for the electrode `M^(n+)|M` with concerntration is given by the expression under `STP` conditions `:`
`E=E^(0)+(0.059)/(n)log[M^(n+)]`

Explanation

To determine whether the statement regarding the electrode potential for the electrode \( M^{n+} | M \) is true or false, we will analyze the expression provided and the conditions under which it holds.

### Step-by-Step Solution:

1. **Understanding the Nernst Equation**:
The Nernst equation is given by:
\[ E = E^0 + \frac{0.059}{n} \log \left[ M^{n+} \right] \]
This equation relates the electrode potential \( E \) to the standard electrode potential \( E^0 \), the number of electrons transferred \( n \), and the concentration of the ion \( M^{n+} \).

2. **Identifying Standard Conditions**:
The term "STP" refers to Standard Temperature and Pressure, which is defined as:
- Standard Temperature: 0 °C (273 K)
- Standard Pressure: 1 atm

3. **Evaluating the Temperature in the Nernst Equation**:
The Nernst equation is typically evaluated at a temperature of 298 K (25 °C) for practical applications. The factor \( 0.059 \) in the equation is derived from the universal gas constant \( R \) and the temperature \( T \) in Kelvin:
\[ E = E^0 - \frac{2.303RT}{nF} \log \left[ \frac{1}{[M^{n+}]} \right] \]
At 298 K, this simplifies to approximately \( 0.059 \) when \( n = 1 \).

4. **Conclusion on the Given Statement**:
The expression \( E = E^0 + \frac{0.059}{n} \log \left[ M^{n+} \right] \) is valid under the condition of 298 K (25 °C) and not at STP (273 K). Therefore, the statement that the expression holds under STP conditions is **false**.

### Final Answer:
The statement is **false**.