The number of consecutive zeros in `2^3xx\ 3^4xx\ 5^4xx\ 7,` is

Options

A. 3
B. 2
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 number 10 can be formed from the factors of the expression. Since \(10 = 2 \times 5\), we will look for pairs of the factors 2 and 5.

### Step-by-step Solution:

1. **Identify the factors**: The expression is given as \(2^3 \times 3^4 \times 5^4 \times 7\).

2. **Count the factors of 2 and 5**:
- The exponent of 2 is 3 (from \(2^3\)).
- The exponent of 5 is 4 (from \(5^4\)).

3. **Form pairs of 2 and 5**:
- Each pair of \(2\) and \(5\) will contribute to one \(10\). Thus, the number of pairs we can form is determined by the smaller of the two exponents.
- Here, we can form \( \min(3, 4) = 3\) pairs of \(2\) and \(5\).

4. **Conclusion**: Since we can form 3 pairs of \(2\) and \(5\), this means there are 3 consecutive zeros in the product \(2^3 \times 3^4 \times 5^4 \times 7\).

Thus, the number of consecutive zeros in the expression is **3**.

### Final Answer:
The number of consecutive zeros is **3**.

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