What should come in place of question mark
`(0.125)^3div(0.25)^2xx(0.5)^2=(0.5)^?`

Options

A. 15
B. 7
C. 18
D. 38

Answer

To solve the equation \( (0.125)^3 \div (0.25)^2 \times (0.5)^2 = (0.5)^{?} \), we will express all terms in the equation using the base \( 0.5 \).

### Step 1: Convert \( 0.125 \) to base \( 0.5 \)
We know that:
\[ 0.125 = \frac{1}{8} = \frac{1}{2^3} = (0.5)^{-3} \]
Thus, we can rewrite \( (0.125)^3 \) as:
\[ (0.125)^3 = ((0.5)^{-3})^3 = (0.5)^{-9} \]

### Step 2: Convert \( 0.25 \) to base \( 0.5 \)
Next, we convert \( 0.25 \):
\[ 0.25 = \frac{1}{4} = \frac{1}{2^2} = (0.5)^{-2} \]
Thus, we can rewrite \( (0.25)^2 \) as:
\[ (0.25)^2 = ((0.5)^{-2})^2 = (0.5)^{-4} \]

### Step 3: Convert \( (0.5)^2 \)
This term is already in the desired form:
\[ (0.5)^2 = (0.5)^2 \]

### Step 4: Substitute back into the equation
Now we can substitute these back into the original equation:
\[ (0.5)^{-9} \div (0.5)^{-4} \times (0.5)^2 = (0.5)^{?} \]

### Step 5: Simplify the left-hand side
Using the property of exponents for division:
\[ (0.5)^{-9} \div (0.5)^{-4} = (0.5)^{-9 - (-4)} = (0.5)^{-9 + 4} = (0.5)^{-5} \]
Now we multiply by \( (0.5)^2 \):
\[ (0.5)^{-5} \times (0.5)^2 = (0.5)^{-5 + 2} = (0.5)^{-3} \]

### Step 6: Set the equation
Now we have:
\[ (0.5)^{-3} = (0.5)^{?} \]
Since the bases are the same, we can equate the exponents:
\[ -3 = ? \]

### Conclusion
Thus, the value of the question mark is:
\[ ? = -3 \]