`(5xx5xx5xx5xx5xx5)^(2)xx(5xx5xx5xx5)^(8)div(5xx5)^(3)=(25)^(?)`

Options

A. 22
B. 13
C. 17
D. 19

Explanation

To solve the equation \((5^{5} \times 5^{5} \times 5^{5} \times 5^{5} \times 5^{5})^{2} \times (5^{5} \times 5^{5} \times 5^{5} \times 5)^{8} \div (5^{5})^{3} = (25)^{?}\), we will follow these steps:

### Step 1: Simplify the base expressions
We can simplify the terms inside the parentheses.

- The first term:
\[ (5^{5} \times 5^{5} \times 5^{5} \times 5^{5} \times 5^{5})^{2} = (5^{5 \times 5})^{2} = (5^{25})^{2} = 5^{50} \]

- The second term:
\[ (5^{5} \times 5^{5} \times 5^{5} \times 5)^{8} = (5^{5 \times 4 + 5})^{8} = (5^{20 + 5})^{8} = (5^{25})^{8} = 5^{200} \]

- The third term:
\[ (5^{5})^{3} = 5^{15} \]

### Step 2: Combine the simplified terms
Now we can substitute these simplified expressions back into the equation:
\[ 5^{50} \times 5^{200} \div 5^{15} \]

Using the properties of exponents, we can combine the terms:
\[ 5^{50 + 200 - 15} = 5^{235} \]

### Step 3: Convert to base 25
Next, we need to express \(5^{235}\) in terms of base \(25\). Since \(25 = 5^{2}\), we can rewrite \(5^{235}\) as:
\[ 5^{235} = (5^{2})^{117.5} = 25^{117.5} \]

### Step 4: Equate to find the unknown
Now we have:
\[ 25^{117.5} = 25^{?} \]
Thus, we can conclude that:
\[ ? = 117.5 \]

### Final Answer
The value of the question mark is:
\[ \boxed{117.5} \]