What value will come in place of both the question marks(?) in the question given below?
`(?^(2))/(128)=(32)/(?^(10))`

Options

A. 16
B. 2
C. 17
D. 19

Answer

To solve the equation \(\frac{x^2}{128} = \frac{32}{x^{10}}\), we will follow these steps:

### Step 1: Set the equation
Let the question mark be represented by \(x\). Therefore, we can rewrite the equation as:

\[ \frac{x^2}{128} = \frac{32}{x^{10}} \]

### Step 2: Cross-multiply
To eliminate the fractions, we will cross-multiply:

\[ x^2 \cdot x^{10} = 32 \cdot 128 \]

### Step 3: Simplify the left side
Using the properties of exponents, we can simplify the left side:

\[ x^{2 + 10} = 32 \cdot 128 \]

This simplifies to:

\[ x^{12} = 32 \cdot 128 \]

### Step 4: Calculate the right side
Now, we need to calculate \(32 \cdot 128\). We can express these numbers as powers of 2:

\[ 32 = 2^5 \quad \text{and} \quad 128 = 2^7 \]

Thus:

\[ 32 \cdot 128 = 2^5 \cdot 2^7 = 2^{5 + 7} = 2^{12} \]

### Step 5: Set the exponents equal
Now we have:

\[ x^{12} = 2^{12} \]

### Step 6: Solve for \(x\)
Since the bases are the same, we can set the exponents equal to each other:

\[ x = 2 \]

### Conclusion
The value that will come in place of both question marks is:

\[ \boxed{2} \]

---