`root(3)((0.000064))` is equal to

Options

A. 0.02
B. 0.2
C. 2
D. 0.04

Answer

To find the cube root of \(0.000064\), we can follow these steps:

### Step 1: Rewrite the number in scientific notation
We can express \(0.000064\) as \(64 \times 10^{-6}\).

### Step 2: Break down the components
We know that \(64\) can be expressed as \(4^3\) because \(4 \times 4 \times 4 = 64\). Therefore, we can rewrite our expression:
\[ 0.000064 = 4^3 \times 10^{-6} \]

### Step 3: Apply the cube root
Now we can take the cube root of both parts:
\[ \sqrt[3]{0.000064} = \sqrt[3]{4^3} \times \sqrt[3]{10^{-6}} \]

### Step 4: Simplify the cube roots
The cube root of \(4^3\) is simply \(4\). For \(10^{-6}\), we can use the property of exponents:
\[ \sqrt[3]{10^{-6}} = 10^{-6/3} = 10^{-2} \]

### Step 5: Combine the results
Now we combine the results:
\[ \sqrt[3]{0.000064} = 4 \times 10^{-2} \]

### Step 6: Convert back to decimal form
Finally, we can convert \(10^{-2}\) back to decimal form:
\[ 4 \times 10^{-2} = 4 \times 0.01 = 0.04 \]

Thus, the cube root of \(0.000064\) is:
\[ \boxed{0.04} \]