Answer
$$4.09\times 10^{21}.$$
Work Step by Step
We have
$$\left(\frac{ 0.259\times 6300 }{866\times 0.013 }\right)^{10}=\left(\frac{ (2.59\times10^{-1})(6.3\times10^3)}{(8.66\times10^2)(1.3\times10^{-2}) }\right)^{10} \\ =\left(\frac{ 1.631\times 10^3}{1.1258\times 10^{1} }\right)^{10}\\ =(1.45\times 10^2)^{10}=4.09\times 10^{21}.$$
