`(4xx4xx4xx4xx4xx4)^(5)xx(4xx4xx4)^(8)div (4)^(3)=(64)^(?)`

Options

A. 17
B. 10
C. 16
D. 11

Explanation

To solve the equation `(4xx4xx4xx4xx4xx4)^(5)xx(4xx4xx4)^(8)div (4)^(3)=(64)^(?)`, we will simplify it step by step.

### Step 1: Rewrite the expression using powers of 4
We know that:
- \(4 = 4^1\)
- \(64 = 4^3\)

Thus, we can rewrite \(64\) as \(4^3\).

The expression becomes:
\[ (4^5)^{5} \times (4^3)^{8} \div (4^3) = (4^3)^{?} \]

### Step 2: Simplify the left side
Using the power of a power property \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[ (4^5)^{5} = 4^{5 \cdot 5} = 4^{25} \]
\[ (4^3)^{8} = 4^{3 \cdot 8} = 4^{24} \]

Now, substituting these back into the expression gives:
\[ 4^{25} \times 4^{24} \div 4^{3} \]

### Step 3: Combine the powers
Using the property \(a^m \times a^n = a^{m+n}\):
\[ 4^{25 + 24} \div 4^{3} = 4^{49} \div 4^{3} \]

### Step 4: Simplify the division
Using the property \(a^m \div a^n = a^{m-n}\):
\[ 4^{49 - 3} = 4^{46} \]

### Step 5: Rewrite in terms of \(64\)
Now we need to express \(4^{46}\) in terms of \(64\):
\[ 4^{46} = (4^3)^{?} \quad \text{since } 64 = 4^3 \]

### Step 6: Set the exponents equal
We know:
\[ 4^{46} = (4^3)^{?} \implies 4^{46} = 4^{3x} \]
Thus, we can set the exponents equal to each other:
\[ 46 = 3x \]

### Step 7: Solve for \(x\)
To find \(x\), divide both sides by 3:
\[ x = \frac{46}{3} = 15.33 \]

### Conclusion
Thus, the value of the question mark is \(x = 15.33\).