Identify like terms in the following:
`-2xy^(2), x^(2)y, 5y^(2)x, x^(2)z`

Answer

To identify the like terms in the given algebraic expressions, we will follow these steps:

### Step 1: Write down the given terms
The terms provided are:
1. \(-2xy^2\)
2. \(x^2y\)
3. \(5y^2x\)
4. \(x^2z\)

### Step 2: Understand what like terms are
Like terms are terms that have the same variable(s) raised to the same power. For example, \(3xy\) and \(5xy\) are like terms because they both have the variables \(x\) and \(y\) raised to the same powers.

### Step 3: Analyze each term
- The first term is \(-2xy^2\). It has \(x\) raised to the power of 1 and \(y\) raised to the power of 2.
- The second term is \(x^2y\). It has \(x\) raised to the power of 2 and \(y\) raised to the power of 1.
- The third term is \(5y^2x\). This can be rearranged as \(5xy^2\), which has \(x\) raised to the power of 1 and \(y\) raised to the power of 2.
- The fourth term is \(x^2z\). It has \(x\) raised to the power of 2 and \(z\) as a variable.

### Step 4: Identify like terms
Now, we compare the terms:
- \(-2xy^2\) and \(5xy^2\) are like terms because they both have \(x\) raised to the power of 1 and \(y\) raised to the power of 2.
- \(x^2y\) and \(x^2z\) are not like terms because they have different variables (\(y\) and \(z\)).
- \(x^2y\) is not like \(-2xy^2\) or \(5xy^2\) because the powers of \(x\) and \(y\) are different.

### Conclusion
The only like terms in the given expressions are:
- \(-2xy^2\) and \(5xy^2\)

### Final Answer
The like terms are:
- \(-2xy^2\) and \(5y^2x\) (which can be written as \(5xy^2\))

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