Answer
$$\frac{2}{p^2q}$$
Work Step by Step
An expression raised to a negative exponent is equivalent to the reciprocal of the expression to that same positive exponent
$$a^{-b}=\frac{1}{a^b}$$
so
$$\frac{4^{1/4}(p^{2/3}q^{-1/3})^{-1}}{4^{-1/4}p^{4/3}q^{4/3}}=\frac{4^{1/4}4^{1/4}q^{1/3}}{p^{2/3}p^{4/3}q^{4/3}}$$
Add exponents when multiplying powers of the same base and subtract when dividing powers of the same base
$$=\frac{4^{(1/4+1/4)}}{p^{(2/3+4/3)}q^{(4/3-1/3)}}=\frac{2}{p^2q}$$
