Answer: \(a=-\frac32\), \(b=\frac83\), \(c=-2\).

Answer: \(a=-\frac32\), \(b=\frac83\), \(c=-2\).

Simplify the numerator first:

\(\sqrt{p q^{4/3}}\,r^{-3}=p^{1/2}q^{2/3}r^{-3}.\)

The denominator is

\((pq^{-1})^2r^{-1}=p^2q^{-2}r^{-1}.\)

When dividing powers, subtract the exponents:

\(\frac{p^{1/2}q^{2/3}r^{-3}}{p^2q^{-2}r^{-1}}=p^{1/2-2}q^{2/3-(-2)}r^{-3-(-1)}.\)

Therefore

\(p^aq^br^c=p^{-3/2}q^{8/3}r^{-2}.\)

Hence \(a=-\frac32\), \(b=\frac83\), and \(c=-2\).