Find the number of terms in
`4xyz-(3)/(x^(2))+6xyz^(2)-5z^(3)+6x:`

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the number of terms in the expression \( 4xyz - \frac{3}{x^2} + 6xyz^2 - 5z^3 + 6x \), we will analyze each part of the expression.

### Step-by-step Solution:

1. **Identify the Expression**:
The given expression is:
\[ 4xyz - \frac{3}{x^2} + 6xyz^2 - 5z^3 + 6x \]

2. **Break Down the Expression**:
We will separate the expression into individual terms. A term is defined as a single mathematical expression that can include numbers, variables, and exponents.

3. **List Each Term**:
- The first term is \( 4xyz \).
- The second term is \( -\frac{3}{x^2} \).
- The third term is \( 6xyz^2 \).
- The fourth term is \( -5z^3 \).
- The fifth term is \( 6x \).

4. **Count the Terms**:
Now, we will count the distinct terms we identified:
- \( 4xyz \) (1st term)
- \( -\frac{3}{x^2} \) (2nd term)
- \( 6xyz^2 \) (3rd term)
- \( -5z^3 \) (4th term)
- \( 6x \) (5th term)

5. **Total Number of Terms**:
Adding these up, we find that there are a total of 5 terms in the expression.

### Final Answer:
The total number of terms in the expression is **5**.

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