Evaluate : `(5^(2))^(6)`

Answer

To evaluate the expression \((5^{2})^{6}\), we can use the exponentiation rule which states that \((a^m)^n = a^{m \cdot n}\).

Here are the steps to solve the problem:

### Step 1: Identify the base and the exponents
In the expression \((5^{2})^{6}\), the base \(a\) is \(5\), \(m\) is \(2\), and \(n\) is \(6\).

### Step 2: Apply the exponentiation rule
Using the rule \((a^m)^n = a^{m \cdot n}\), we can rewrite the expression as:
\[ (5^{2})^{6} = 5^{2 \cdot 6} \]

### Step 3: Calculate the exponent
Now, calculate \(2 \cdot 6\):
\[ 2 \cdot 6 = 12 \]

### Step 4: Rewrite the expression
Now we can rewrite the expression with the new exponent:
\[ (5^{2})^{6} = 5^{12} \]

### Step 5: Calculate \(5^{12}\)
To find the value of \(5^{12}\), we can calculate it step by step or use a calculator. The value of \(5^{12}\) is:
\[ 5^{12} = 244140625 \]

### Final Answer
Thus, the evaluated result of \((5^{2})^{6}\) is:
\[ 5^{12} = 244140625 \]

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