Question

Como chego nesse resultado?

Answer 1

Tentei resumir ao máximo de forma clara.
$\ \ \ \ 8^{-\frac{2}{3}}+\sqrt{0,25}+4\cdot(0,5)^4\\ \\=(2^3)^{-\frac{2}{3}}+\sqrt{ \frac{25}{100} }+4\cdot( \frac{5}{10} )^4\\ \\=2^{-\frac{3\cdot2}{3}}+\frac{5}{10}+4\cdot( \frac{5^{:5}}{10_{:5}} )^4\\ \\=2^{-\frac{6}{3}}+\frac{5^{:5}}{10_{:5}}+4\cdot( \frac{1}{2})^4\\ \\=2^{-2}+\frac{1}{2}+4\cdot\frac{1}{16}\\ \\=(\frac{1}{2})^2+\frac{1}{2}+\frac{4^{:4}}{16_{:4}}\\ \\=\frac{1}{4}+\frac{1}{2}+\frac{1}{4}\\ \\=\frac{1}{4}+\frac{2}{4}+\frac{1}{4}\\ \\=\frac{1+2+1}{4}\\ \\=\frac{4}{4}\\ \\=1$