Factor to find variables with even exponents: $\displaystyle\sqrt{{{{f}}^{{12}}\cdot{f{\cdot}}{{g}}^{{8}}\cdot{g{\cdot}}{{h}}^{{10}}}}\usepackage{cmbright}\Huge\$

Rewrite those as squares: $\displaystyle\sqrt{{{{\left({{f}}^{{6}}\right)}}^{{2}}\cdot{f{\cdot}}{{\left({{g}}^{{4}}\right)}}^{{2}}\cdot{g{\cdot}}{{\left({{h}}^{{5}}\right)}}^{{2}}}}\usepackage{cmbright}\Huge\$

Separate the squares into individual radicals: $\displaystyle\sqrt{{{{\left({{f}}^{{6}}\right)}}^{{2}}}}\cdot\sqrt{{{{\left({{g}}^{{4}}\right)}}^{{2}}}}\cdot\sqrt{{{{\left({{h}}^{{5}}\right)}}^{{2}}}}\cdot\sqrt{{{f{\cdot}}{g}}}\usepackage{cmbright}\Huge\$

Find square roots. Use absolute value for odd exponents: $\displaystyle{{f}}^{{6}}\cdot{{g}}^{{4}}\cdot{\left|{{h}}^{{5}}\right|}\cdot\sqrt{{{f{\cdot}}{g}}}\usepackage{cmbright}\Huge\$

Simplify: $\displaystyle{{f}}^{{6}}{{g}}^{{4}}{\left|{{h}}^{{5}}\right|}\sqrt{{{f{{g}}}}}\usepackage{cmbright}\Huge\$