The number of consecutive zeros in `2^3xx3^4xx5^4xx7` is equal to:

Options

A. 2
B. 3
C. 4
D. 5

Answer

To find the number of consecutive zeros in the expression \(2^3 \times 3^4 \times 5^4 \times 7\), we need to determine how many times the factors 10 can be formed from the prime factorization of the expression. Since \(10 = 2 \times 5\), we need to find the minimum of the number of 2s and 5s in the factorization.

### Step-by-Step Solution:

1. **Identify the prime factorization**:
The expression is already given in its prime factorization form:
\[ 2^3 \times 3^4 \times 5^4 \times 7 \]

2. **Count the factors of 2 and 5**:
- From \(2^3\), we have 3 factors of 2.
- From \(5^4\), we have 4 factors of 5.

3. **Determine the number of pairs of (2, 5)**:
To form a 10, we need one factor of 2 and one factor of 5. Thus, the number of tens (which corresponds to the number of consecutive zeros) is determined by the limiting factor, which in this case is the number of 2s:
\[ \text{Number of tens} = \min(\text{Number of 2s}, \text{Number of 5s}) = \min(3, 4) = 3 \]

4. **Conclusion**:
Therefore, the number of consecutive zeros in the expression \(2^3 \times 3^4 \times 5^4 \times 7\) is:
\[ \boxed{3} \]