${\left(2^{-5}\right)}^2=2^{-5\cdot 2}=2^{-10}$

${\left(4^{-3}\right)}^{-8}=4^{-3\cdot \left(-8\right)}=4^{24}={\left(2^2\right)}^{24}=2^{2\cdot 24}=2^{48}$ ${\left(4^{-3}\right)}^{-8}=4^{-3\cdot \left(-8\right)}=4^{24}={\left(2^2\right)}^{24}=2^{2\cdot 24}=2^{48}$

${\left[{\left(\frac{1}{2}\right)}^9\right]}^5={\left(\frac{1}{2}\right)}^{9\cdot 5}={\left(\frac{1}{2}\right)}^{45}$

${\left(2^3\right)}^6=2^{3\cdot 6}=2^{18}$

${\left[{\left(\frac{1}{4}\right)}^9\right]}^{-1}={\left(\frac{1}{4}\right)}^{-9}=4^9={\left(2^2\right)}^9=2^{2\cdot 9}=2^{18}$

${\left[{\left(\frac{1}{2}\right)}^{-1}\right]}^{-10}={\left(\frac{1}{2}\right)}^{-1\cdot \left(-10\right)}={\left(\frac{1}{2}\right)}^{10}=2^{-10}$

${\left({16}^3\right)}^4={16}^{3\cdot 4}={16}^{12}={\left(2^4\right)}^{12}=2^{4\cdot 12}=2^{48}$

${\left[{\left(\frac{1}{8}\right)}^{-5}\right]}^{-3}={\left(8^5\right)}^{-3}=8^{5\cdot \left(-3\right)}=8^{-15}={\left(2^3\right)}^{-15}=2^{-45}={\left(\frac{1}{2}\right)}^{45}$