The value of `(-0.4)^(3)` is

Options

A. `0.640`
B. 0.064
C. -0.064
D. `-0.640`

Answer

To find the value of \((-0.4)^3\), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ (-0.4)^3 \]

### Step 2: Rewrite the decimal
To simplify calculations, we can rewrite \(-0.4\) as a fraction:
\[ -0.4 = -\frac{4}{10} \]

### Step 3: Cube the fraction
Now, we will cube the fraction:
\[ (-0.4)^3 = \left(-\frac{4}{10}\right)^3 \]

### Step 4: Apply the power to the numerator and denominator
Cubing the fraction means we cube both the numerator and the denominator:
\[ \left(-\frac{4}{10}\right)^3 = \frac{(-4)^3}{(10)^3} \]

### Step 5: Calculate the cubes
Now, we calculate the cubes:
\[ (-4)^3 = -64 \quad \text{and} \quad (10)^3 = 1000 \]
So we have:
\[ \frac{-64}{1000} \]

### Step 6: Simplify the fraction
The fraction \(\frac{-64}{1000}\) can be expressed as a decimal:
\[ \frac{-64}{1000} = -0.064 \]

### Final Answer
Thus, the value of \((-0.4)^3\) is:
\[ \boxed{-0.064} \]

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