Exponential quiz

(2^-4 + 4^-3)/2^-3

$\begin{array}{rcll} \dfrac{ 2^{-4} + 4^{-3} } { 2^{-3} } &=& 2^3\cdot ( 2^{-4} + 4^{-3} ) \\\\ &=& 2^3\cdot [ 2^{-4} + (2\cdot 2)^{-3} ] \\\\ &=& 2^3\cdot [ 2^{-4} + (2^2)^{-3} ] \\\\ &=& 2^3\cdot [ 2^{-4} + 2^{2\cdot (-3)} ]\\\\ &=& 2^3\cdot [ 2^{-4} + 2^{-6} ]\\\\ &=& 2^3\cdot 2^{-4} + 2^3\cdot 2^{-6} \\\\ &=& 2^{3-4} + 2^{3-6} \\\\ &=& 2^{-1} + 2^{-3} \\\\ &=& \frac{1}{2} + \frac{1}{2^3} \\\\ &=& \frac{1}{2} + \frac{1}{8} \\\\ &=& \frac{1}{2}\cdot \frac{4}{4} + \frac{1}{8} \\\\ &=& \frac{4}{8} + \frac{1}{8} \\\\ &=& \frac{4+1}{8} \\\\ &=& \frac{5}{8} \\\\ &=& 0.625 \\\\ \end{array}$