Lời giải của Tự Học 365

${{x}^{\frac{4}{5}}}\sqrt[6]{{{x}^{5}}\sqrt{x}}$ $={{x}^{\frac{4}{5}}}\sqrt[6]{{{x}^{5}}{{x}^{\frac{1}{2}}}}$ $={{x}^{\frac{4}{5}}}\sqrt[6]{{{x}^{5+\frac{1}{2}}}}$ $={{x}^{\frac{4}{5}}}{{\left( {{x}^{\frac{11}{2}}} \right)}^{\frac{1}{6}}}$ $={{x}^{\frac{4}{5}}}{{x}^{\frac{11}{2}.\frac{1}{6}}}$ $={{x}^{\frac{4}{5}}}{{x}^{\frac{11}{12}}}$ $={{x}^{\frac{4}{5}+\frac{11}{12}}}$ $={{x}^{\frac{103}{60}}}={{x}^{m}}$ $\Rightarrow m=\dfrac{103}{60}$

$\begin{align}{{y}^{\frac{4}{5}}}:\sqrt[6]{{{y}^{5}}\sqrt{y}}={{y}^{\frac{4}{5}}}:\sqrt[6]{{{y}^{5}}{{y}^{\frac{1}{2}}}}\\={{y}^{\frac{4}{5}}}:\sqrt[6]{{{y}^{5+\frac{1}{2}}}}\\={{y}^{\frac{4}{5}}}:{{\left( {{y}^{\frac{11}{2}}} \right)}^{\frac{1}{6}}}={{y}^{\frac{4}{5}}}:{{y}^{\frac{11}{2}.\frac{1}{6}}}\\={{y}^{\frac{4}{5}}}:{{y}^{\frac{11}{12}}}={{y}^{\frac{4}{5}-\frac{11}{12}}}\\={{y}^{-\frac{7}{60}}}={{y}^{n}}\\\Rightarrow n=-\frac{7}{60} \\  \Rightarrow m-n=\frac{103}{60}-\frac{-7}{60}=\frac{11}{6} \\ \end{align}$

Đáp án cần chọn là: c