Answer:
[tex]=536870912[/tex]
Step-by-step explanation:
[tex]\frac{\left(2^3\right)^{10}\cdot \:2^{-8}}{2^{-7}}\\\mathrm{Cancel\:}\frac{\left(2^3\right)^{10}\cdot \:2^{-8}}{2^{-7}}:\quad \frac{\left(2^3\right)^{10}}{2}\\\frac{\left(2^3\right)^{10}\cdot \:2^{-8}}{2^{-7}}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}\\\frac{2^{-8}}{2^{-7}}=\frac{1}{2^{-7-\left(-8\right)}}\\=\frac{\left(2^3\right)^{10}}{2^{-7-\left(-8\right)}}\\\mathrm{Subtract\:the\:numbers:}\:-7-\left(-8\right)=\\=\frac{\left(2^3\right)^{10}}{2}[/tex]
[tex]\mathrm{Simplify\:}\left(2^3\right)^{10}:\quad 2^{30}\\\left(2^3\right)^{10}\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\=2^{3\cdot \:10}\\\mathrm{Multiply\:the\:numbers:}\:3\cdot \:10=30\\=2^{30}\\=\frac{2^{30}}{2}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=2^{29}\\2^{29}=536870912\\=536870912[/tex]
