The total number of prime factors in expression `(6)^(10)xx(7)^(17)xx(11)^(27)` is

Options

A. 654
B. 64
C. 71
D. 81

Answer

To find the total number of prime factors in the expression \( (6)^{10} \times (7)^{17} \times (11)^{27} \), we will break down the steps as follows:

### Step 1: Identify the prime factors in the expression
The expression consists of three parts:
- \( (6)^{10} \)
- \( (7)^{17} \)
- \( (11)^{27} \)

Now, we need to identify the prime factors in each part:
- The number \( 6 \) can be factored into prime factors as \( 2 \times 3 \).
- The number \( 7 \) is already a prime number.
- The number \( 11 \) is also a prime number.

Thus, the prime factors in the expression are \( 2, 3, 7, \) and \( 11 \).

### Step 2: Count the distinct prime factors
From the prime factorization, we have identified the following distinct prime factors:
1. \( 2 \)
2. \( 3 \)
3. \( 7 \)
4. \( 11 \)

### Step 3: Calculate the total number of prime factors
Now, we can count the total number of distinct prime factors:
- There are 4 distinct prime factors: \( 2, 3, 7, \) and \( 11 \).

### Conclusion
Therefore, the total number of prime factors in the expression \( (6)^{10} \times (7)^{17} \times (11)^{27} \) is **4**.

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