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

Options

A. (a) `frac(-3)(2)`
B. (b) `frac(-1)(8)`
C. (c) `frac(-1)(6)`
D. (d) none of these

Answer

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

### Step 1: Write the expression
We start with the expression:
\[ \left(-\frac{1}{2}\right)^3 \]

### Step 2: Expand the exponent
The exponent 3 means we will multiply \(-\frac{1}{2}\) by itself three times:
\[ \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) \]

### Step 3: Multiply the numerators
Now, we multiply the numerators:
\[ -1 \times -1 \times -1 = -1 \]

### Step 4: Multiply the denominators
Next, we multiply the denominators:
\[ 2 \times 2 \times 2 = 8 \]

### Step 5: Combine the results
Now we combine the results from the numerators and denominators:
\[ \frac{-1}{8} \]

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

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