Solve the parameter from a symmetric exponential identity: If (p/q)^(n−1) = (q/p)^(n−3), determine the value of n.

Introduction / Context:This problem hinges on properties of exponents and reciprocals. Recognizing that (q/p) = (p/q)^(−1) converts the equation to a simple equality of exponents, allowing quick solution for n.Given Data / Assumptions:

• (p/q)^(n−1) = (q/p)^(n−3).
• Assume p and q are nonzero and p/q > 0 so real powers are defined.

Concept / Approach:Rewrite (q/p)^(n−3) as (p/q)^(−(n−3)). Since the bases match and are positive and not 1, we equate exponents directly.Step-by-Step Solution:

Verification / Alternative check:Substitute n = 2: LHS = (p/q)^(1) = p/q; RHS = (q/p)^(−1) = p/q. Both sides match.

Why Other Options Are Wrong:

• 1/2, 7/2, 1: These do not satisfy the exponent equation and fail upon substitution.

Common Pitfalls:Forgetting that (q/p) = (p/q)^(−1) or mishandling the minus sign when moving exponents across the equality.

Final Answer: