a) mϵ {510;512;514;516;518;520;522;524}.

b) m ϵ {510;515;520;525}.

c) m ϵ {510;520}.

Bước rút gọn  là sai vì không có tính chất  .

Sửa lại như sau: 

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Ta có: \(\left(0,125\right)^3\cdot8^3+\left(\frac34-\frac56\right)^2-\frac{50^3}{125}+20^5\cdot\frac{5^{10}}{100^5}\)

\(=\left(0,125\cdot8\right)^3+\left(\frac{9}{12}-\frac{10}{12}\right)^2-\frac{\left(5^2\cdot2\right)^3}{5^3}+\frac{5^5\cdot2^{10}\cdot5^{10}}{\left(2^2\cdot5^2\right)^5}\)

\(=1+\left(-\frac{1}{12}\right)^2-\frac{5^6\cdot2^3}{5^3}+5^5=1+\frac{1}{144}-5^3\cdot2^3+5^5\)

\(=\frac{145}{144}+5^3\left(5^2-2^3\right)=\frac{145}{144}+125\cdot17=\frac{306145}{144}\)

Ta có: \(\left(0,125\right)^3\cdot8^3+\left(\frac34-\frac56\right)^2-\frac{50^3}{125}+20^5\cdot\frac{5^{10}}{100^5}\)

\(=\left(0,125\cdot8\right)^3+\left(\frac{9}{12}-\frac{10}{12}\right)^2-\frac{\left(5^2\cdot2\right)^3}{5^3}+\frac{5^5\cdot2^{10}\cdot5^{10}}{\left(2^2\cdot5^2\right)^5}\)

\(=1+\left(-\frac{1}{12}\right)^2-\frac{5^6\cdot2^3}{5^3}+5^5=1+\frac{1}{144}-5^3\cdot2^3+5^5\)

\(=\frac{145}{144}+5^3\left(5^2-2^3\right)=\frac{145}{144}+125\cdot17=\frac{306145}{144}\)

Ta có: \(\left(0,125\right)^3\cdot8^3+\left(\frac34-\frac56\right)^2-\frac{50^3}{125}+20^5\cdot\frac{5^{10}}{100^5}\)

\(=\left(0,125\cdot8\right)^3+\left(\frac{9}{12}-\frac{10}{12}\right)^2-\frac{\left(5^2\cdot2\right)^3}{5^3}+\frac{5^5\cdot2^{10}\cdot5^{10}}{\left(2^2\cdot5^2\right)^5}\)

\(=1+\left(-\frac{1}{12}\right)^2-\frac{5^6\cdot2^3}{5^3}+5^5=1+\frac{1}{144}-5^3\cdot2^3+5^5\)

\(=\frac{145}{144}+5^3\left(5^2-2^3\right)=\frac{145}{144}+125\cdot17=\frac{306145}{144}\)