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 incorrectly obtained $\displaystyle{120}{\left(\frac{{3}}{{2}}\right)}\usepackage{cmbright}\Huge\$ . The correct answer is 15.