Evalution : `root3(-0.000008/(-0.000216))`

Options

A. 3
B. `-1//3`
C. `-3`
D. `1//3`

Answer

To solve the expression \( \sqrt[3]{\frac{-0.000008}{-0.000216}} \), we can follow these steps:

### Step 1: Simplify the expression
We start with the expression:
\[ \sqrt[3]{\frac{-0.000008}{-0.000216}} \]
Since both the numerator and the denominator are negative, the negatives will cancel out:
\[ \sqrt[3]{\frac{0.000008}{0.000216}} \]

### Step 2: Convert the decimal numbers to scientific notation
We can express the numbers in scientific notation:
- \( 0.000008 = 8 \times 10^{-6} \)
- \( 0.000216 = 216 \times 10^{-6} \)

Now we can rewrite the expression:
\[ \sqrt[3]{\frac{8 \times 10^{-6}}{216 \times 10^{-6}}} \]

### Step 3: Cancel out the common terms
The \( 10^{-6} \) in the numerator and denominator can be canceled:
\[ \sqrt[3]{\frac{8}{216}} \]

### Step 4: Simplify the fraction
Now we simplify \( \frac{8}{216} \):
\[ \frac{8}{216} = \frac{1}{27} \]

### Step 5: Find the cube root
Now we find the cube root:
\[ \sqrt[3]{\frac{1}{27}} = \frac{1}{\sqrt[3]{27}} = \frac{1}{3} \]

### Final Answer
Thus, the final answer is:
\[ \frac{1}{3} \]