https://file.aiquickdraw.com/mathbot/file/17260246295807iecl55m.jpg

Let's break down the expression provided in the image:

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

### Step-by-step simplification:

1. **Combine like terms**:
   - For the \(x\) terms: \(x^2 \cdot x^2 = x^{2+2} = x^4\).
   - The numerator becomes: \(x^4 y\).

2. **Simplify the \(y\) terms**:
   - In the denominator, you have \(y^{-4}\). 
   - Using the property of exponents \(\frac{y}{y^{-4}} = y^{1 - (-4)} = y^5\).

Thus, the simplified expression is:

\[
x^4 y^5
\]

Now, let's compare it with the options given. The correct equivalent expression is:

\[
x^4 y^5
\]

So the correct answer is the last option: \(x^4 y^5\).

Would you like further details or clarifications?

Here are five related questions to consider:
1. How do you simplify expressions with negative exponents?
2. What are the rules for multiplying variables with exponents?
3. How do you simplify a fraction with terms in the numerator and denominator?
4. Can you explain the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\)?
5. What happens when you raise a variable to a zero exponent?

**Tip**: Always simplify terms with the same base by adding or subtracting their exponents according to their positions (numerator/denominator).

Select the equivalent expression: (x^2 * x^2 * y) / y^(-4)

Learn how to simplify an algebraic expression with exponents. This example demonstrates the key rules of exponents, including multiplying and dividing terms with the same base. Suitable for students in Grades 8-10.

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