What must come in the place of ? in the given equation?

\(\sqrt {{{\left( {243} \right)}^{\frac{4}{5}}}} \times \sqrt {{{324}^2}} \div {2^{ - 4}}\ = \frac{{{6^{{?^2} + 5}}}}{{{6^3}}}\)

Option 1 : 2

\(\sqrt {{{\left( {243} \right)}^{\frac{4}{5}}}} \times \sqrt {{{324}^2}}\div {2^{ - 4}}\ = \frac{{{6^{{?^2} + 5}}}}{{{6^3}}}\)

\(\sqrt {{{243}^{\frac{4}{5}}}} = {3^{\frac{{10}}{5}}} = {3^2}\)

\(\sqrt {{{324}^2}} = {18^2} = {3^4} \times {2^2}\)

\(\Rightarrow {3^2} \times {3^4} \times {2^2} \times {2^4} = {6^{{x^2} + 5 - 3}}\)

⇒ x^{2 }= 6 – 2

⇒ x = 2