Regroup the factors: $\displaystyle{\left({9.16}\times{5.5}\right)}{\left({{10}}^{{-{{3}}}}\times{{10}}^{{10}}\right)}\usepackage{cmbright}\Huge\$

Multiply the numbers: $\displaystyle{\left({50.38}\right)}{\left({{10}}^{{-{{3}}}}\times{{10}}^{{10}}\right)}\usepackage{cmbright}\Huge\$

Use the product rule: $\displaystyle{50.38}\times{{10}}^{{-{3}+{10}}}={50.38}\times{{10}}^{{7}}\usepackage{cmbright}\Huge\$

Convert 50.38 into scientific notation: $\displaystyle{\left({5.038}\times{{10}}^{{1}}\right)}\times{{10}}^{{7}}\usepackage{cmbright}\Huge\$

Regroup and use the product rule: $\displaystyle{5.038}\times{\left({{10}}^{{1}}\times{{10}}^{{7}}\right)}={5.038}\times{{10}}^{{{1}+{7}}}={5.038}\times{{10}}^{{8}}\usepackage{cmbright}\Huge\$