Regroup the factors and multiply the numbers: $\displaystyle{\left({5}\times{8.4}\right)}{\left({{10}}^{{-{{11}}}}\times{{10}}^{{7}}\right)}={\left({42}\right)}{\left({{10}}^{{-{{11}}}}\times{{10}}^{{7}}\right)}\usepackage{cmbright}\Huge\$

Use the product rule: $\displaystyle{42}\times{{10}}^{{-{11}+{7}}}={42}\times{{10}}^{{-{{4}}}}\usepackage{cmbright}\Huge\$

Convert 42 to $\displaystyle{4.2}\times{{10}}^{{1}}\usepackage{cmbright}\Huge\$ , regroup, and multiply: $\displaystyle{4.2}\times{\left({{10}}^{{1}}\times{{10}}^{{-{{4}}}}\right)}={4.2}\times{{10}}^{{{1}+{\left(-{4}\right)}}}={4.2}\times{{10}}^{{-{{3}}}}\usepackage{cmbright}\Huge\$