https://file.aiquickdraw.com/mathbot/file/1725420861134a5bq5616.jpg

The image shows the following expression to be simplified:

\[
\frac{x^2 y}{y^{-3}} \times \frac{x^{-4} y^3}{x^{-3}}
\]

Let's simplify this step by step.

### Step 1: Simplify the first fraction
\[
\frac{x^2 y}{y^{-3}} = x^2 y^{1 - (-3)} = x^2 y^{4}
\]

### Step 2: Simplify the second fraction
\[
\frac{x^{-4} y^3}{x^{-3}} = x^{-4 - (-3)} y^3 = x^{-1} y^3
\]

### Step 3: Multiply the simplified expressions
\[
x^2 y^{4} \times x^{-1} y^{3} = x^{2 - 1} y^{4 + 3} = x^{1} y^{7}
\]

Thus, the simplified expression is:

\[
x y^7
\]

If you have any questions or need further details, feel free to ask!

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**Related Questions:**
1. How do you simplify expressions with negative exponents?
2. What are the rules for multiplying terms with the same base?
3. How do you handle expressions with multiple variables and exponents?
4. Can you explain the properties of exponents used in this problem?
5. How would the solution change if there were more variables in the expression?

**Tip:** Always simplify expressions within fractions first before multiplying or dividing them to avoid unnecessary complications.

Simplify the expression \(\frac{x^2 y}{y^{-3}} \times \frac{x^{-4} y^3}{x^{-3}}\)

Simplify the expression \(\frac{x^2 y}{y^{-3}} \times \frac{x^{-4} y^3}{x^{-3}}\) with detailed steps. This problem covers key algebraic concepts, including the use of exponent rules and properties. Perfect for students in Grades 9-11.

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