If `((1)/(5))^(3y)=0.008`, then the value of `(0.25)^(y)` is

Options

A. `0.25`
B. `6.25`
C. `2.5`
D. `53`

Answer

To solve the equation \(\left(\frac{1}{5}\right)^{3y} = 0.008\) and find the value of \((0.25)^{y}\), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \left(\frac{1}{5}\right)^{3y} = 0.008 \]
We can express \(0.008\) in terms of fractions. Notice that:
\[ 0.008 = \frac{8}{1000} = \frac{1}{125} \]

### Step 2: Express \(0.008\) as a power of \(\frac{1}{5}\)
Next, we can express \(\frac{1}{125}\) as a power of \(\frac{1}{5}\):
\[ \frac{1}{125} = \left(\frac{1}{5}\right)^3 \]
Thus, we can rewrite the equation as:
\[ \left(\frac{1}{5}\right)^{3y} = \left(\frac{1}{5}\right)^3 \]

### Step 3: Set the exponents equal to each other
Since the bases are the same, we can equate the exponents:
\[ 3y = 3 \]

### Step 4: Solve for \(y\)
Now, we can solve for \(y\) by dividing both sides by 3:
\[ y = 1 \]

### Step 5: Find \((0.25)^{y}\)
Now that we have the value of \(y\), we can find \((0.25)^{y}\):
\[ (0.25)^{y} = (0.25)^{1} = 0.25 \]

### Final Answer
Thus, the value of \((0.25)^{y}\) is:
\[ \boxed{0.25} \]