Identify like terms in the following:
`abc, ab^(2)c, acb^(2), c^(2)ab, b^(2)ac, a^(2)bc, cab^(2)`

Answer

To identify like terms from the given expressions, we need to look for terms that have the same variables raised to the same powers. Let's analyze the terms one by one.

### Step-by-Step Solution:

1. **List the Terms**:
The given terms are:
- \( abc \)
- \( ab^2c \)
- \( acb^2 \)
- \( c^2ab \)
- \( b^2ac \)
- \( a^2bc \)
- \( cab^2 \)

2. **Identify the Variables and Their Powers**:
- \( abc \): \( a^1b^1c^1 \)
- \( ab^2c \): \( a^1b^2c^1 \)
- \( acb^2 \): \( a^1b^2c^1 \) (same as \( ab^2c \))
- \( c^2ab \): \( a^1b^1c^2 \)
- \( b^2ac \): \( a^1b^2c^1 \) (same as \( ab^2c \) and \( acb^2 \))
- \( a^2bc \): \( a^2b^1c^1 \)
- \( cab^2 \): \( a^1b^2c^1 \) (same as \( ab^2c \), \( acb^2 \), and \( b^2ac \))

3. **Group the Like Terms**:
- The terms \( ab^2c \), \( acb^2 \), \( b^2ac \), and \( cab^2 \) all have the same variables with the same powers: \( a^1b^2c^1 \).
- The term \( abc \) is unique with \( a^1b^1c^1 \).
- The term \( c^2ab \) is unique with \( a^1b^1c^2 \).
- The term \( a^2bc \) is unique with \( a^2b^1c^1 \).

4. **Final List of Like Terms**:
- Like terms: \( ab^2c \), \( acb^2 \), \( b^2ac \), \( cab^2 \)
- Unique terms: \( abc \), \( c^2ab \), \( a^2bc \)

### Conclusion:
The like terms in the given expressions are:
- \( ab^2c \)
- \( acb^2 \)
- \( b^2ac \)
- \( cab^2 \)