You may have substituted correctly to obtain

$\displaystyle{R}={120}{{\left(\frac{{1}}{{2}}\right)}}^{{\frac{{24}}{{8}}}}={120}{{\left(\frac{{1}}{{2}}\right)}}^{{3}}\usepackage{cmbright}\Huge\$

but then did not follow the correct order of operations. Be sure to raise $\displaystyle\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ to the given power first and then multiply by 120. The correct answer is 15.