#### Answer

$a^{3}b^{7}c$

#### Work Step by Step

$\sqrt[3] (a^{9}b^{21}c^{3})=\sqrt[3] (a^{9}\times b^{21}\times c^{3})=\sqrt[3] (a^{9})\times \sqrt[3] (b^{21})\times \sqrt[3] (c^{3})=a^{3}b^{7}c$
$\sqrt[3] (a^{9})=a^{3}$, because $(a^{3})^{3}=a^{3\times3}=a^{9}$
$\sqrt[3] (b^{21})=b^{7}$, because $(b^{7})^{3}=b^{7\times3}=b^{21}$
$\sqrt[3] (c^{3})=c$, because $(c)^{3}=c^{3}$