tìm x thỏa mãn ( $\frac{3}{2x}$ – $\frac{5}{2})^{60}$ = $(\frac{1}{8})^{20}$ : $(-\frac{1}{4})^{10}$

Ta có

$\left( \dfrac{3}{2x} – \dfrac{5}{2} \right)^{60} = \left( \dfrac{1}{8} \right)^{20} : \left( -\dfrac{1}{4} \right)^{10}$

$<-> \left( \dfrac{3}{2x} – \dfrac{5}{2} \right)^{60} = \dfrac{1}{(2^3)^{20}} : \dfrac{1}{(2^2)^{10}}$

$<-> \left( \dfrac{3}{2x} – \dfrac{5}{2} \right)^{60} =\dfrac{2^{20}}{2^{60}}$

$<-> \left( \dfrac{3}{2x} – \dfrac{5}{2} \right)^{60} = \dfrac{1}{2^{40}}$

$<-> \dfrac{3}{2x} – \dfrac{5}{2} = \pm \dfrac{1}{\sqrt[3]{4}}$

$<-> \dfrac{3}{2x} = \dfrac{5}{2} \pm \dfrac{1}{\sqrt[3]{4}}$

$<-> \dfrac{3}{x} = 5 \pm \sqrt[3]{2}$

$<-> x = \dfrac{3}{5 \pm \sqrt[3]{2}}$

Vậy $x = \dfrac{3}{5 \pm \sqrt[3]{2}}$.