Answer: \(\displaystyle \frac38p^{-2}q^{3/2}r^{-16/5}\), so \(k=\frac38\), \(a=-2\), \(b=\frac32\), \(c=-\frac{16}{5}\).

Answer: \(\displaystyle \frac38p^{-2}q^{3/2}r^{-16/5}\), so \(k=\frac38\), \(a=-2\), \(b=\frac32\), \(c=-\frac{16}{5}\).

Rewrite the expression using index notation:

Now divide powers with the same base:

\(\frac{3p}{8p^3}=\frac38p^{-2},\)

\(\frac{q^{1/2}}{q^{-1}}=q^{1/2-(-1)}=q^{3/2},\)

and

\(\frac{r^{-3}}{r^{1/5}}=r^{-3-\frac15}=r^{-16/5}.\)

Therefore the expression is

\(\frac38p^{-2}q^{3/2}r^{-16/5}.\)