Question

please answer the question

Answer 1

$\bigg[\dfrac{2}{3} \bigg]^6 \times\bigg [\dfrac{2}{3}\bigg]^{-2} \times \bigg [\dfrac{4}{9}\bigg]^{-2}$

$= \bigg[\dfrac{2}{3} \bigg]^6 \times\bigg [\dfrac{3}{2}\bigg]^{2} \times \bigg [\dfrac{9}{4}\bigg]^{2}$

$= \dfrac{2^6}{3^6} \times \dfrac{3^2}{2^2} \times \dfrac{9^2}{4^2}$

$= \dfrac{2^6 \times 2^2 \times 9^2}{3^6 \times 2^2 \times 4^2}$

$= \dfrac{2^6 \times 2^2 \times 3^4}{3^6 \times 2^2 \times 2^4}$

$= 2^{6 + 2 - 2+4} \times 3^{4-6}$

$= 2^{10} \times 3^{-2}$

$= \dfrac{2^{10}}{3^2}$