#### Answer

$3a\sqrt[4] {2a}$

#### Work Step by Step

$3\sqrt[4] {32a^{5}}-a\sqrt[4] {162a}$
=$3\sqrt[4] {16\times2\times a^{4}\times a}-a\sqrt[4] {81\times 2 \times a}$
=$3\sqrt[4] {2^{4}\times a^{4}\times 2\times a}-a\sqrt[4] {3^{4}\times 2 \times a}$
=$3(\sqrt[4] {2^{4}\times a^{4}}\times \sqrt[4] {2\times a})-a(\sqrt[4] {3^{4}}\times \sqrt[4] {2 \times a})$
=$3(2a\times \sqrt[4] {2a})-a(3\times \sqrt[4] {2a})$
=$6a\sqrt[4] {2a}-3a\sqrt[4] {2a}$
=$(6a-3a)\sqrt[4] {2a}$
=$3a\sqrt[4] {2a}$