Simplify combining like terms:
`-z^(2) +13z^(2) - 5z + 7z^(3) -15z`

Answer

To simplify the expression `-z^(2) + 13z^(2) - 5z + 7z^(3) - 15z`, we will combine like terms step by step.

### Step 1: Identify Like Terms
First, we need to identify the like terms in the expression. Like terms are terms that have the same variable raised to the same power.

- The terms with \( z^3 \): \( 7z^3 \)
- The terms with \( z^2 \): \( -z^2 \) and \( 13z^2 \)
- The terms with \( z \): \( -5z \) and \( -15z \)

### Step 2: Combine the Like Terms
Now we will combine the like terms:

1. **For \( z^3 \)**:
- There is only one term: \( 7z^3 \)
- So, it remains \( 7z^3 \).

2. **For \( z^2 \)**:
- Combine \( -z^2 \) and \( 13z^2 \):
\[ -1z^2 + 13z^2 = (13 - 1)z^2 = 12z^2 \]

3. **For \( z \)**:
- Combine \( -5z \) and \( -15z \):
\[ -5z - 15z = -(5 + 15)z = -20z \]

### Step 3: Write the Final Expression
Now we can write the simplified expression by combining all the results:
\[ 7z^3 + 12z^2 - 20z \]

### Final Answer
The simplified expression is:
\[ 7z^3 + 12z^2 - 20z \]

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