from sympy import symbols, simplify

Define the variables

x, y, z = symbols('x y z')

Define the expression

expression = (x * z2) * (-2 * x3 * y2 * 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.