In order to simplify this expression, we can use the following property:
[tex]\begin{gathered} \frac{1}{a^b}=a^{-b} \\ a^b\cdot a^c=a^{b+c} \end{gathered}[/tex]
Simplifying the given expression using only positive exponents, we have:
[tex]\begin{gathered} \frac{2^3a^{-3}}{8^{-1}b^{-5}c^0} \\ =\frac{2^3}{a^38^{-1}b^{-5}c^0} \\ =\frac{2^3\cdot2^3}{a^3b^{-5}c^0} \\ =\frac{2^3\cdot2^3\cdot b^5}{a^3} \\ =\frac{2^{3+3}\cdot b^5}{a^3} \\ =\frac{2^6b^5}{a^3} \end{gathered}[/tex]
