Simplify the following expressions.
`(5^(2))^(3)`

Answer

To simplify the expression \((5^{2})^{3}\), we will use the exponentiation rule which states that \((a^{m})^{n} = a^{m \cdot n}\).

### Step-by-Step Solution:

1. **Identify the base and the exponents**:
Here, the base is \(5\), and the exponents are \(2\) and \(3\).

2. **Apply the exponentiation rule**:
According to the rule, we can rewrite the expression as:
\[ (5^{2})^{3} = 5^{2 \cdot 3} \]

3. **Calculate the new exponent**:
Now, multiply the exponents:
\[ 2 \cdot 3 = 6 \]
So, we have:
\[ (5^{2})^{3} = 5^{6} \]

4. **Final result**:
Therefore, the simplified expression is:
\[ 5^{6} \]

### Answer:
The value of the given expression is \(5^{6}\).