Divide the masses, regroup, divide the numbers, and use the quotient rule:

$\displaystyle\frac{{{1.9}\times{{10}}^{{27}}}}{{{6}\times{{10}}^{{24}}}}={\left(\frac{{1.9}}{{6}}\right)}{\left(\frac{{{10}}^{{27}}}{{{10}}^{{24}}}\right)}={0.317}\times{{10}}^{{{27}-{24}}}={0.317}\times{{10}}^{{3}}\usepackage{cmbright}\Huge\$

Convert 0.317 to scientific notation, regroup, and use the product rule: $\displaystyle{3.17}\times{\left({{10}}^{{-{{1}}}}\times{{10}}^{{3}}\right)}={3.17}\times{{10}}^{{-{1}+{3}}}={3.17}\times{{10}}^{{2}}\usepackage{cmbright}\Huge\$