Use the Distributive Property:

$\displaystyle{\sqrt[{{3}}]{{{{y}}^{{2}}}}}{\left({5}{\sqrt[{{3}}]{{{y}}}}+{\sqrt[{{3}}]{{{{y}}^{{4}}}}}-{9}{\sqrt[{{3}}]{{{8}{y}}}}\right)}={\left({\sqrt[{{3}}]{{{{y}}^{{2}}}}}\right)}{\left({5}{\sqrt[{{3}}]{{{y}}}}\right)}+{\left({\sqrt[{{3}}]{{{{y}}^{{2}}}}}\right)}{\left({\sqrt[{{3}}]{{{{y}}^{{4}}}}}\right)}-{\left({\sqrt[{{3}}]{{{{y}}^{{2}}}}}\right)}{\left({9}{\sqrt[{{3}}]{{{8}{y}}}}\right)}\usepackage{cmbright}\Huge\$

$\displaystyle={5}{\sqrt[{{3}}]{{{{y}}^{{3}}}}}+{\sqrt[{{3}}]{{{{y}}^{{6}}}}}-{9}{\sqrt[{{3}}]{{{8}{{y}}^{{3}}}}}={5}{\sqrt[{{3}}]{{{{y}}^{{3}}}}}+{\sqrt[{{3}}]{{{{\left({{y}}^{{2}}\right)}}^{{3}}}}}-{9}{\sqrt[{{3}}]{{{8}}}}\cdot{\sqrt[{{3}}]{{{{y}}^{{3}}}}}\usepackage{cmbright}\Huge\$

$\displaystyle={5}\cdot{y}+{{y}}^{{2}}-{9}\cdot{2}\cdot{y}={5}{y}+{{y}}^{{2}}-{18}{y}={{y}}^{{2}}-{13}{y}\usepackage{cmbright}\Huge\$