Answer:
x = 2
Step-by-step explanation:
[tex] \bigg( \frac{3}{4} \bigg)^{6} \times\bigg( \frac{16}{9} \bigg)^{5} = \bigg( \frac{4}{3} \bigg)^{x + 2} \\ \\ \bigg( \frac{3}{4} \bigg)^{6} \times\bigg( \frac{ {4}^{2} }{ {3}^{2} } \bigg)^{5} = \bigg( \frac{4}{3} \bigg)^{x + 2} \\ \\ \frac{ {3}^{6} }{ {4}^{6} } \times \frac{ {4}^{10} }{ {3}^{10} } = \bigg( \frac{4}{3} \bigg)^{x + 2} \\ \\ \frac{ {4}^{10 - 6} }{ {3}^{10 - 6} } = \bigg( \frac{4}{3} \bigg)^{x + 2} \\ \\ \frac{ {4}^{4} }{ {3}^{4} } = \bigg( \frac{4}{3} \bigg)^{x + 2} \\ \\ \bigg( \frac{4}{3} \bigg)^{4} = \bigg( \frac{4}{3} \bigg)^{x + 2} \\ \\ \implies \: 4 = x + 2 \\ \\ \implies \: x = 4 - 2 \\ \\ \implies \: x = 2[/tex]
