a
Explanation
Step 1
remember some laws of exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]
then
[tex]2^{-5}\cdot2^8=2^{-5+8}=2^3=8[/tex]
now, check the answer options
[tex]\begin{gathered} a)\frac{2^2}{2^{-1}}=2^2\cdot\frac{1}{2^{-1}}=4\cdot2=8 \\ b)(2^3)^{-1}=2^{3\cdot-1}=2^{-3}=\frac{1}{2^3}=\frac{1}{8} \\ c)\frac{2^{-2}}{2^{-1}}=\frac{2^1}{2^2}=\frac{2}{4}=\frac{1}{2} \\ d)(2^{-1})^3=2^{1-\cdot3}=2^{-3}=\frac{1}{2^3}=\frac{1}{8} \end{gathered}[/tex]
so, the answer is a
