Siimplify:- 2 * 256 * ? = 8^2 * 10^2 * 2

Options

A. a. 60
B. b. 50
C. c. 46
D. d. none of these

Answer

To solve the equation \(2 \times 256 \times ? = 8^2 \times 10^2 \times 2\), we will follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ 2 \times 256 \times ? = 8^2 \times 10^2 \times 2 \]

### Step 2: Simplify the right side
First, we need to simplify the right side of the equation:
\[ 8^2 = 8 \times 8 = 64 \]
\[ 10^2 = 10 \times 10 = 100 \]
So,
\[ 8^2 \times 10^2 \times 2 = 64 \times 100 \times 2 \]

### Step 3: Calculate \(64 \times 100 \times 2\)
Now, we calculate:
\[ 64 \times 100 = 6400 \]
Then,
\[ 6400 \times 2 = 12800 \]
Thus, the right side simplifies to:
\[ 8^2 \times 10^2 \times 2 = 12800 \]

### Step 4: Set up the equation with the simplified right side
Now we have:
\[ 2 \times 256 \times ? = 12800 \]

### Step 5: Isolate the question mark
To find \(?\), we can rearrange the equation:
\[ ? = \frac{12800}{2 \times 256} \]

### Step 6: Calculate \(2 \times 256\)
First, calculate \(2 \times 256\):
\[ 2 \times 256 = 512 \]

### Step 7: Substitute back into the equation
Now substitute back into the equation:
\[ ? = \frac{12800}{512} \]

### Step 8: Perform the division
Now, divide \(12800\) by \(512\):
\[ ? = 25 \]

### Final Answer
Thus, the value of \(?\) is:
\[ \boxed{25} \]

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