Cube of `((-1)/4)` is

Options

A. `(-1)/12`
B. `1/16`
C. `(-1)/64`
D. `1/64`

Answer

To find the cube of \((-1/4)\), we can follow these steps:

### Step 1: Write the expression for the cube
We need to calculate the cube of \((-1/4)\). This can be expressed as:
\[ \left(-\frac{1}{4}\right)^3 \]

### Step 2: Apply the property of exponents
Using the property of exponents, we can separate the numerator and the denominator:
\[ \left(-\frac{1}{4}\right)^3 = \frac{(-1)^3}{4^3} \]

### Step 3: Calculate \((-1)^3\)
Now, we calculate \((-1)^3\):
\[ (-1)^3 = -1 \]
Since the exponent is odd, the result is negative.

### Step 4: Calculate \(4^3\)
Next, we calculate \(4^3\):
\[ 4^3 = 4 \times 4 \times 4 = 64 \]

### Step 5: Combine the results
Now, we can combine the results from steps 3 and 4:
\[ \left(-\frac{1}{4}\right)^3 = \frac{-1}{64} \]

### Final Answer
Thus, the cube of \((-1/4)\) is:
\[ -\frac{1}{64} \]

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