Evaluate : `(2^(3))^(4)`

Answer

To evaluate the expression \((2^3)^4\), we can follow these steps:

### Step 1: Identify the base and the exponents
The expression \((2^3)^4\) consists of a base \(2\) raised to the power of \(3\), and this entire expression is raised to the power of \(4\).

### Step 2: Apply the exponentiation rule
According to the exponentiation rule, \((a^m)^n = a^{m \cdot n}\). Here, we can apply this rule:
\[ (2^3)^4 = 2^{3 \cdot 4} \]

### Step 3: Multiply the exponents
Now, we need to multiply the exponents:
\[ 3 \cdot 4 = 12 \]
So, we can rewrite the expression as:
\[ (2^3)^4 = 2^{12} \]

### Step 4: Calculate \(2^{12}\)
Now we need to evaluate \(2^{12}\). This can be calculated as follows:
\[ 2^{12} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \]
Calculating this gives:
\[ 2^{12} = 4096 \]

### Final Answer
Thus, the value of \((2^3)^4\) is \(4096\).

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