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Let's solve the given expression:

\[
\frac{(6u^3y^5 - 13u^7y^5)}{-2u^5y^4}
\]

### Step 1: Break the expression into two fractions

We can split the numerator into two terms and divide each by the denominator:

\[
\frac{6u^3y^5}{-2u^5y^4} - \frac{13u^7y^5}{-2u^5y^4}
\]

### Step 2: Simplify each term separately

#### First term: \(\frac{6u^3y^5}{-2u^5y^4}\)

- Coefficients: \(\frac{6}{-2} = -3\)
- For the \(u\) terms: \(\frac{u^3}{u^5} = u^{3-5} = u^{-2}\)
- For the \(y\) terms: \(\frac{y^5}{y^4} = y^{5-4} = y^1 = y\)

Thus, the first term simplifies to:

\[
-3u^{-2}y = \frac{-3y}{u^2}
\]

#### Second term: \(\frac{13u^7y^5}{-2u^5y^4}\)

- Coefficients: \(\frac{13}{-2} = -\frac{13}{2}\)
- For the \(u\) terms: \(\frac{u^7}{u^5} = u^{7-5} = u^2\)
- For the \(y\) terms: \(\frac{y^5}{y^4} = y^{5-4} = y\)

Thus, the second term simplifies to:

\[
-\frac{13}{2} u^2 y
\]

### Step 3: Combine the results

Now, combining both simplified terms:

\[
\frac{-3y}{u^2} + \left(-\frac{13}{2} u^2 y\right)
\]

This is the fully simplified form of the given expression.

Would you like further clarification or any details on this? Here are some related questions:

1. How do you handle exponents when dividing terms with the same base?
2. What happens if the exponent is negative in the final answer?
3. How can we combine terms when dividing a polynomial by a monomial?
4. How does the process change when dealing with coefficients in division?
5. What are some tips for simplifying algebraic expressions with multiple variables?

**Tip:** When simplifying terms with exponents, always subtract exponents of like bases during division.

Divide: (6u^3y^5 - 13u^7y^5) ÷ (-2u^5y^4). Simplify your answer as much as possible.

Learn how to simplify the expression (6u^3y^5 - 13u^7y^5) ÷ (-2u^5y^4) using division of polynomials and exponent rules. This detailed guide walks through each step of the simplification process, demonstrating how to handle exponents and combine like terms.

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