Find the Domain ((x^5y^2)/(wz^3))-3

Problem

(x5*y2)/(w*z3)−3

Solution

1. Identify the variables in the expression. The expression involves four variables: x y w and z

2. Analyze the structure of the expression. The expression is a rational function where the denominator is w*z3

3. Determine the constraints for the domain. In a rational expression, the denominator cannot be equal to zero because division by zero is undefined.

4. Set the denominator equal to zero to find the excluded values.

w*z3=0

5. Solve for the variables. By the zero product property, the product is zero if either w=0 or z3=0

w=0

z=0

6. State the domain. The domain consists of all real numbers for x y w and z such that w≠0 and z≠0

Final Answer

Domain={(x,y,w,z)∈ℝ4:w≠0,z≠0}

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