Evaluate : `(-2)^(3)xx4^(3)`

Answer

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

### Step 1: Rewrite \(4\) in terms of base \(2\)
We know that \(4\) can be expressed as \(2^{2}\). Therefore, we can rewrite the expression as:
\[ (-2)^{3} \times (2^{2})^{3} \]

### Step 2: Apply the power of a power rule
Using the exponent rule \((a^{m})^{n} = a^{m \times n}\), we can simplify \((2^{2})^{3}\):
\[ (-2)^{3} \times 2^{2 \times 3} = (-2)^{3} \times 2^{6} \]

### Step 3: Separate the bases
Now, we can express \((-2)^{3}\) as:
\[ (-1)^{3} \times 2^{3} \]
Thus, our expression becomes:
\[ (-1)^{3} \times 2^{3} \times 2^{6} \]

### Step 4: Combine the powers of \(2\)
Using the property \(a^{m} \times a^{n} = a^{m+n}\), we combine the powers of \(2\):
\[ (-1)^{3} \times 2^{3 + 6} = (-1)^{3} \times 2^{9} \]

### Step 5: Calculate the final result
Now, we know that \((-1)^{3} = -1\), so we can write:
\[ -1 \times 2^{9} = -2^{9} \]
Calculating \(2^{9}\):
\[ 2^{9} = 512 \]
Thus, the final result is:
\[ -512 \]

### Final Answer:
\[ (-2)^{3} \times 4^{3} = -512 \]

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