State whether a given pair of terms is of like or unlike terms.
`4m^(2)p, 4mp^(2)`

Answer

To determine whether the given pair of terms \(4m^2p\) and \(4mp^2\) are like or unlike terms, we will follow these steps:

### Step 1: Identify the terms
The two terms we have are:
1. \(4m^2p\)
2. \(4mp^2\)

### Step 2: Analyze the variable parts
We need to focus on the variable parts of each term, ignoring the coefficients (the numbers in front of the variables).

- For the first term \(4m^2p\), the variable part is \(m^2p\).
- For the second term \(4mp^2\), the variable part is \(mp^2\).

### Step 3: Compare the variable parts
Now, we will compare the variable parts:
- In \(m^2p\), the variable \(m\) has an exponent of 2.
- In \(mp^2\), the variable \(m\) has an exponent of 1, and the variable \(p\) has an exponent of 2.

### Step 4: Determine if they are like or unlike
For the terms to be considered like terms, the variable parts must be identical in both terms, including the powers of each variable.

- The variable \(m\) in the first term has a power of 2, while in the second term it has a power of 1.
- The variable \(p\) is present in both terms but with different powers (1 in the first term and 2 in the second term).

Since the powers of the variables are not the same, we conclude that the terms are unlike.

### Conclusion
The terms \(4m^2p\) and \(4mp^2\) are **unlike terms**.

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