`(0.01024)^((1)/(5))=`_____

Options

A. `sqrt(0.4)`
B. `0.2`
C. `0.4`
D. `3sqrt0.4`

Explanation

To solve the expression \( (0.01024)^{\frac{1}{5}} \), we will follow these steps:

### Step 1: Rewrite the decimal in a more manageable form
First, we can express \( 0.01024 \) as a fraction. Since \( 0.01024 \) can be rewritten as \( \frac{1024}{100000} \), we have:
\[ 0.01024 = \frac{1024}{100000} \]

### Step 2: Factor the numerator and denominator
Next, we can factor \( 1024 \) and \( 100000 \) into powers of 2 and 10:
- \( 1024 = 2^{10} \)
- \( 100000 = 10^5 = (10^2)^5 = 100^5 \)

Thus, we can rewrite \( 0.01024 \) as:
\[ 0.01024 = \frac{2^{10}}{10^5} \]

### Step 3: Rewrite the expression with the new fraction
Now we can substitute this fraction back into our original expression:
\[ (0.01024)^{\frac{1}{5}} = \left(\frac{2^{10}}{10^5}\right)^{\frac{1}{5}} \]

### Step 4: Apply the power of a quotient rule
Using the power of a quotient rule, we can separate the powers:
\[ = \frac{(2^{10})^{\frac{1}{5}}}{(10^5)^{\frac{1}{5}}} \]

### Step 5: Simplify the powers
Now we simplify the powers:
- For the numerator: \( (2^{10})^{\frac{1}{5}} = 2^{10 \cdot \frac{1}{5}} = 2^2 = 4 \)
- For the denominator: \( (10^5)^{\frac{1}{5}} = 10^{5 \cdot \frac{1}{5}} = 10^1 = 10 \)

Thus, we have:
\[ = \frac{4}{10} \]

### Step 6: Simplify the fraction
Now we can simplify \( \frac{4}{10} \):
\[ \frac{4}{10} = 0.4 \]

### Final Answer
Therefore, the value of \( (0.01024)^{\frac{1}{5}} \) is:
\[ \boxed{0.4} \]