Let's simplify the expression:

\[
\frac{(-y)^4}{(-y^{-3})^5} \times y^2
\]

### Step 1: Simplify powers of \(-y\)

Start with the powers of \(-y\):

- \((-y)^4\) becomes \((-1)^4 \cdot y^4 = y^4\) because \((-1)^4 = 1\).

Now simplify \((-y^{-3})^5\):

\[
(-y^{-3})^5 = (-1)^5 \cdot (y^{-3})^5 = -y^{-15}
\]

The expression becomes:

\[
\frac{y^4}{-y^{-15}} \times y^2
\]

### Step 2: Simplify the fraction

Now simplify the fraction:

\[
\frac{y^4}{-y^{-15}} = -y^{4 - (-15)} = -y^{4 + 15} = -y^{19}
\]

So the expression becomes:

\[
-y^{19} \times y^2
\]

### Step 3: Multiply the remaining terms

Now multiply:

\[
-y^{19} \times y^2 = -y^{19 + 2} = -y^{21}
\]

### Final Answer:

\[
\boxed{-y^{21}}
\]

Would you like more details or have any questions?

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Here are five related questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for multiplying powers of the same base?
3. How do you handle powers of negative numbers?
4. Can you explain how to simplify more complex fractions with exponents?
5. How do you simplify expressions involving multiple powers and negative signs?

**Tip**: When dealing with negative exponents, remember that \(y^{-n} = \frac{1}{y^n}\), and flipping the exponent sign can simplify your calculations.

Explore the step-by-step solution to simplifying the expression (-y)^4 ÷ (-y^-3)^5 x y^2 using exponentiation rules. This guide covers concepts like negative exponents, power of powers, and multiplication of powers, making it suitable for Grades 9-11 students.

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