Challenger

$\frac {7^2 \times 9^3}{27 \times 343}$

= $\frac {7^2 \times 9^3}{3^3 \times 7^3}$

= $\frac {7^2 \times (3^{2)^3}}{3^3 \times 7^3}$

= $\frac {7^2 \times 3^6}{3^3 \times 7^3}$

= $\frac {3^3}{7}$

= 27/7