Cube of `-1/2` is

Options

A. `1/8`
B. `1/16`
C. `-1/8`
D. `-1/16`

Answer

To find the cube of \(-\frac{1}{2}\), we can follow these steps:

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

### Step 2: Apply the property of exponents
Using the property of exponents that states \((a \cdot b)^m = a^m \cdot b^m\), we can separate the terms:
\[ \left(-1 \cdot \frac{1}{2}\right)^3 = (-1)^3 \cdot \left(\frac{1}{2}\right)^3 \]

### Step 3: Calculate \((-1)^3\)
Now, we calculate \((-1)^3\):
\[ (-1)^3 = -1 \]

### Step 4: Calculate \(\left(\frac{1}{2}\right)^3\)
Next, we calculate \(\left(\frac{1}{2}\right)^3\) using the property \(\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}\):
\[ \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8} \]

### Step 5: Combine the results
Now we can combine the results from Step 3 and Step 4:
\[ (-1) \cdot \frac{1}{8} = -\frac{1}{8} \]

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

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