State whether a given pair of terms is of like or unlike terms.
`12xz, 12x^(2)z^(2)`

Answer

To determine whether the given pair of terms, `12xz` and `12x^2z^2`, are like or unlike terms, we can follow these steps:

### Step 1: Identify the Terms
The two terms we are examining are:
- Term 1: `12xz`
- Term 2: `12x^2z^2`

### Step 2: Analyze the Variable Parts
Next, we need to look at the variable parts of both terms:
- For `12xz`, the variable part is `xz`.
- For `12x^2z^2`, the variable part is `x^2z^2`.

### Step 3: Compare the Variables and Their Powers
Now, we will compare the variables and their powers:
- In `12xz`, the variable `x` has a power of 1 (since it is not explicitly written, it is understood to be 1).
- In `12x^2z^2`, the variable `x` has a power of 2, and `z` has a power of 2.

### Step 4: Determine Like or Unlike Terms
For the terms to be like terms, both the variable parts and their powers must be the same. Here, we see:
- The variable `x` has different powers (1 in the first term and 2 in the second term).
- The variable `z` also has 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.

### Final Conclusion
The given pair of terms `12xz` and `12x^2z^2` are **unlike terms**.

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