The simplest one

$\Large{{\sqrt[3]{\dfrac{3^6\times 4^3 \times 2^6}{8^9 \times 2^3}} \\ =\dfrac{3^{\frac{6}{3}} \times 4^{\frac{3}{3}}\times 2^{\frac{6}{3}}}{8^{\frac{9}{3}} \times 2^{\frac{3}{3}}}} \\ =\dfrac{3^2 \times 4 \times 2^2}{8^3 \times 2} \\ =\dfrac{3^2 \times 2^2 \times 2^2}{2^9 \times 2} \\ = \dfrac{3^2\times 2^4}{2^{10}} \\ =\dfrac{3^2}{2^6} \\ =\boxed{\dfrac{9}{64}}}$

$\Large \color{#3D99F6}{\sqrt[3]{\dfrac{3^6 \times 4^3 \times 2^6}{8^9 \times 2^3}}=\ ? }$

We can also write this as $\Large \color{#EC7300}{\sqrt[3]{\dfrac{3^6 \times 2^{6}\times 2^6}{2^{30}}}} \\ =\Large \color{#20A900}{\dfrac{12^{\frac{6}{3}}}{2^{\frac{30}{3}}}}\\ =\color{#3D99F6}{ \dfrac{144}{1024}}\\ = \color{#D61F06}{\boxed{\dfrac{9}{64}}}$

$=\sqrt [ 3 ]{ \frac { { 3 }^{ 6 }\cdot { 4 }^{ 3 }\cdot { 2 }^{ 6 } }{ { 8 }^{ 9 }\cdot { 2 }^{ 3 } } } \\ =\sqrt [ 3 ]{ \frac { { 3 }^{ 6 }\cdot { 2 }^{ 6 }\cdot { 2 }^{ 6 } }{ { 2 }^{ 27 }\cdot { 2 }^{ 3 } } } \\ =\sqrt [ 3 ]{ \frac { { 3 }^{ 6 }\cdot { 2 }^{ 12 } }{ { 2 }^{ 30 } } } \\ =\sqrt [ 3 ]{ \frac { { 3 }^{ 6 } }{ { 2 }^{ 18 } } } \\ =\sqrt [ 3 ]{ \frac { { ({ 3 }^{ 2 }) }^{ 3 } }{ { ({ 2 }^{ 6 }) }^{ 3 } } } \\ =\frac { { 3 }^{ 2 } }{ { 2 }^{ 6 } } \\ =\frac { 9 }{ 64 }$

Lol so easy

😂😂😂

without any help I solve the problem......