List of the like terms in the following expression.
(i) `4x^(4),-7x^(3),8x^(2),12x^(3),-9x^(4),-5x,4x^(3),12x^(2)`
`(ii) 5xy,-3x^(2)y,2xy^(3),-2x^(2)y^(2),5x^(2)y,-3xy,6x^(2)y^(2)`

Explanation

To solve the problem of identifying like terms in the given expressions, we will follow these steps:

### Step 1: Identify Like Terms in Expression (i)

The first expression is:
\[ 4x^{4}, -7x^{3}, 8x^{2}, 12x^{3}, -9x^{4}, -5x, 4x^{3}, 12x^{2} \]

1. **Group the terms based on their variables and exponents**:
- **For \(x^4\)**: \(4x^4\) and \(-9x^4\)
- **For \(x^3\)**: \(-7x^3\), \(12x^3\), and \(4x^3\)
- **For \(x^2\)**: \(8x^2\) and \(12x^2\)
- **For \(x\)**: \(-5x\)

2. **List the like terms**:
- Like terms for \(x^4\): \(4x^4, -9x^4\)
- Like terms for \(x^3\): \(-7x^3, 12x^3, 4x^3\)
- Like terms for \(x^2\): \(8x^2, 12x^2\)
- The term \(-5x\) does not have any like terms.

### Step 2: Identify Like Terms in Expression (ii)

The second expression is:
\[ 5xy, -3x^{2}y, 2xy^{3}, -2x^{2}y^{2}, 5x^{2}y, -3xy, 6x^{2}y^{2} \]

1. **Group the terms based on their variables**:
- **For \(xy\)**: \(5xy\) and \(-3xy\)
- **For \(x^2y\)**: \(-3x^2y\) and \(5x^2y\)
- **For \(xy^3\)**: \(2xy^3\) (no like terms)
- **For \(x^2y^2\)**: \(-2x^2y^2\) and \(6x^2y^2\)

2. **List the like terms**:
- Like terms for \(xy\): \(5xy, -3xy\)
- Like terms for \(x^2y\): \(-3x^2y, 5x^2y\)
- Like terms for \(x^2y^2\): \(-2x^2y^2, 6x^2y^2\)
- The term \(2xy^3\) does not have any like terms.

### Final List of Like Terms

- **From Expression (i)**:
- \(4x^4, -9x^4\)
- \(-7x^3, 12x^3, 4x^3\)
- \(8x^2, 12x^2\)

- **From Expression (ii)**:
- \(5xy, -3xy\)
- \(-3x^2y, 5x^2y\)
- \(-2x^2y^2, 6x^2y^2\)