Solve {left({left(1/sqrt[7]{{left({left(frac{1{27}right)}^{3/4}right)}^{-2/3}}}right)}^{5/3}right)}^{{x}^frac{-2{3}}({left(frac{9}{{2187}^frac{-3{2}}}right)}^frac{5{3}}}={19683}^frac{3{4}}

$${ \left( { \left( \frac{ 1 }{ \sqrt[ 7 ]{ { \left( { \left( \frac{ 1 }{ 27 } \right) }^{ \frac{ 3 }{ 4 } } \right) }^{ - \frac{ 2 }{ 3 } } } } \right) }^{ \frac{ 5 }{ 3 } } \right) }^{ { x }^{ \frac{ -2 }{ 3 } } ( { \left( \frac{ 9 }{ { 2187 }^{ \frac{ -3 }{ 2 } } } \right) }^{ \frac{ 5 }{ 3 } } } = { 19683 }^{ \frac{ 3 }{ 4 } }$$

Solve for x (complex solution)

$$x=\frac{61767339628394700}{7}i\times 3^{\frac{1}{4}}\times 70^{-\frac{1}{2}}\left(27\ln(3)+8in_{1}\pi \right)^{-\frac{3}{2}}\ln(3)^{\frac{3}{2}}\text{, }n_{1}\in \mathrm{Z}\text{, }|arg(\left(56i\pi \times 3^{\frac{1}{6}}n_{1}+189\times 3^{\frac{1}{6}}\ln(3)\right)\times \left(617673396283947000i\left(1890\ln(3)+560in_{1}\pi \right)^{-\frac{3}{2}}\right)^{\frac{2}{3}})+\left(-1\right)\pi |<\frac{2}{3}\pi$$

$$x=\left(-\frac{61767339628394700}{7}i\right)\times 3^{\frac{1}{4}}\times 70^{-\frac{1}{2}}\left(27\ln(3)+8in_{1}\pi \right)^{-\frac{3}{2}}\ln(3)^{\frac{3}{2}}\text{, }n_{1}\in \mathrm{Z}\text{, }|arg(\left(56i\pi \times 3^{\frac{1}{6}}n_{1}+189\times 3^{\frac{1}{6}}\ln(3)\right)\times \left(\left(-617673396283947000i\right)\left(1890\ln(3)+560in_{1}\pi \right)^{-\frac{3}{2}}\right)^{\frac{2}{3}})+\left(-1\right)\pi |<\frac{2}{3}\pi$$