`(- (1)/(2)) ^(3)` = ?

Options

A. `(-1)/(6)`
B. `1/6`
C. `1/8`
D. `(-1)/(8)`

Answer

To solve the expression \((- \frac{1}{2})^{3}\), we will follow these steps:

### Step 1: Understand the expression
The expression \((- \frac{1}{2})^{3}\) means that we need to multiply \(- \frac{1}{2}\) by itself three times.

### Step 2: Write out the multiplication
\[ (- \frac{1}{2})^{3} = (- \frac{1}{2}) \times (- \frac{1}{2}) \times (- \frac{1}{2}) \]

### Step 3: Multiply the first two terms
First, we multiply the first two terms:
\[ (- \frac{1}{2}) \times (- \frac{1}{2}) = \frac{1}{4} \]
(The product of two negative numbers is positive.)

### Step 4: Multiply the result with the third term
Now, we multiply \(\frac{1}{4}\) by the third term:
\[ \frac{1}{4} \times (- \frac{1}{2}) = -\frac{1}{8} \]
(Here, we multiply a positive number by a negative number, which results in a negative number.)

### Final Answer
Thus, the value of \((- \frac{1}{2})^{3}\) is:
\[ -\frac{1}{8} \]

### Summary
The final answer is \(-\frac{1}{8}\).

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