If q^(-a) = 1/r and r^(-b) = 1/s and s^(-c) = 1/q, the value of abc is:

A. (rqs)^(-1) B. 0 C. 1 D. r + q + s

Question

If q^(-a) = 1/r and r^(-b) = 1/s and s^(-c) = 1/q, the value of abc is:

A. (rqs)^(-1)  B. 0  C. 1  D. r + q + s

Accepted Answer

The value of abc is 1. Each of the three equations has the form base^(-exponent) = 1/next_variable, which rewrites as base^exponent = next_variable. Together, they form a cycle: q goes to r, r goes to s, and s goes back to q. Chaining all three substitutions gives q^(abc) = q, so abc must equal 1.