https://file.aiquickdraw.com/mathbot/file/1725066091266ostwth85.jpg

from sympy import symbols, simplify

# Define the variables
x, y, z = symbols('x y z')

# Define the expression
expression = (x * z**2) * (-2 * x**3 * y**2 * z)**(-2)

# Simplify the expression
simplified_expression = simplify(expression)
simplified_expressionThe given expression simplifies to:

\[
\frac{1}{4x^5y^4}
\]

Would you like an explanation of the steps involved in this simplification, or do you have any further questions?

Here are five related questions that might interest you:

1. What would happen if the exponent \(-2\) were \(-3\) instead?
2. How does the expression change if \( y = 0 \)?
3. Can this expression be rewritten with positive exponents?
4. How would the simplification differ if the original expression included a fractional coefficient?
5. What is the impact on the expression if \( z \) is a function of another variable?

**Tip:** Be careful with negative exponents—reversing their sign typically involves taking the reciprocal of the base.

Learn how to simplify an expression involving exponents and negative exponents. This problem demonstrates simplification techniques for complex algebraic expressions, focusing on exponents and their properties. Suitable for high school students in Grades 11-12.

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