What will come in place of the question mark (?) in the following questions ?
`784xx7sqrt((256))xx343=4^4xx7^?`

Options

A. 3
B. 6
C. 9
D. 5

Answer

To solve the equation \( 784 \times 7 \times \sqrt{256} \times 343 = 4^4 \times 7^? \), we will break it down step by step.

### Step 1: Simplify the left-hand side
First, we need to simplify \( \sqrt{256} \):
\[ \sqrt{256} = 16 \]
Now, we can rewrite the left-hand side:
\[ 784 \times 7 \times 16 \times 343 \]

### Step 2: Factor the numbers
Next, we can factor the numbers:
- \( 784 = 28^2 = (4 \times 7)^2 = 4^2 \times 7^2 \)
- \( 343 = 7^3 \)

Now substituting these values back into the equation:
\[ (4^2 \times 7^2) \times 7 \times 16 \times (7^3) \]

### Step 3: Simplify further
Now, we can replace \( 16 \) with \( 4^2 \):
\[ (4^2 \times 7^2) \times 7 \times (4^2) \times (7^3) \]
Combine the terms:
\[ 4^2 \times 4^2 = 4^{2+2} = 4^4 \]
And for the \( 7 \) terms:
\[ 7^2 \times 7^1 \times 7^3 = 7^{2+1+3} = 7^6 \]

So, the left-hand side simplifies to:
\[ 4^4 \times 7^6 \]

### Step 4: Set the equation
Now we can set the left-hand side equal to the right-hand side:
\[ 4^4 \times 7^6 = 4^4 \times 7^? \]

### Step 5: Equate the powers
Since the bases are the same, we can equate the powers of \( 7 \):
\[ 6 = ? \]

Thus, the value that comes in place of the question mark is:
\[ ? = 6 \]

### Final Answer
The answer is \( 6 \).

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