GATE CS 2018 QGA-7 — General Aptitude

We are given the following three equations:

1. $p^{-x} = \dfrac{1}{q} \implies p^{-x} = q^{-1} \implies q = p^x$
2. $q^{-y} = \dfrac{1}{r} \implies q^{-y} = r^{-1} \implies r = q^y$
3. $r^{-z} = \dfrac{1}{p} \implies r^{-z} = p^{-1} \implies p = r^z$

Now, we can substitute the expression for $q$ from the first equation into the second equation:

Next, substitute this expression for $r$ into the third equation:

Since $p = p^1$, comparing the exponents on both sides gives:

Thus, the value of the product $xyz$ is $1$.