Identify which of the following algebraic expressions are polynomials. If so, write their degrees.
`(2)/(5)-(3)/(7)x^(3)+5xy^(3)-(1)/(2)z^(5)`

Answer

To determine if the given algebraic expression is a polynomial and to find its degree, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Expression**: The expression given is:
\[ \frac{2}{5} - \frac{3}{7}x^3 + 5xy^3 - \frac{1}{2}z^5 \]

2. **Check Each Term**: A polynomial is defined as an expression where all the variables have whole number powers (non-negative integers). Let's check each term:
- The first term is \(\frac{2}{5}\), which is a constant and can be considered as \( \frac{2}{5}x^0 \).
- The second term is \(-\frac{3}{7}x^3\), where the power of \(x\) is 3 (a whole number).
- The third term is \(5xy^3\). Here, \(x\) has a power of 1 and \(y\) has a power of 3 (both are whole numbers).
- The fourth term is \(-\frac{1}{2}z^5\), where the power of \(z\) is 5 (a whole number).

3. **Conclusion on Polynomial**: Since all the terms in the expression have variables raised to whole number powers, the entire expression is a polynomial.

4. **Find the Degree**: The degree of a polynomial is the highest power of any variable in the expression. In our case:
- The powers of the variables are:
- \(x\): 3
- \(y\): 3
- \(z\): 5
- The highest power among these is 5 (from the term \(-\frac{1}{2}z^5\)).

5. **Final Answer**:
- The expression is a polynomial.
- The degree of the polynomial is 5.

### Summary:
- The expression is a polynomial.
- The degree of the polynomial is 5.