`axxaxxaxxbxxbxxb` is equal to

Options

A. `a^(2)b^(3)`
B. `a^(3)b^(2)`
C. `(ab)^(3)`
D. `a^(6)b^(6)`

Answer

To solve the expression `axxaxxaxxbxxbxxb`, we will follow these steps:

1. **Identify the Variables**: The expression consists of the variables `a` and `b`. We will count how many times each variable appears.

2. **Count the Occurrences of `a`**:
- Looking at the expression, we see `a` appears 3 times.
- We can write this as \( a^3 \).

3. **Count the Occurrences of `b`**:
- Next, we count how many times `b` appears.
- In the expression, `b` appears 3 times as well.
- We can write this as \( b^3 \).

4. **Combine the Results**:
- Now we can combine the results for `a` and `b` into a single expression.
- This gives us \( a^3 \times b^3 \).

5. **Final Expression**:
- We can also express the final answer using the property of exponents, which states that \( x^m \times y^m = (xy)^m \).
- Thus, we can write \( a^3 \times b^3 \) as \( (ab)^3 \).

So, the final answer is:

\[ a^3 b^3 \quad \text{or} \quad (ab)^3 \]