Question

If $[{\left(\frac{3}{4}\right)}^3\times \frac{3}{4}]+{\left(\frac{16}{9}\right)}^2=\frac{7209m}{20736}$.Find $m$

Answer 1

$[{\left(\frac{3}{4}\right)}^3\times \frac{3}{4}]+{\left(\frac{16}{9}\right)}^2=\frac{7209m}{20736}$

$\Rightarrow \left[{\left(\frac{3}{4}\right)}^4\right]+{\left(\frac{16}{9}\right)}^2=\frac{7209m}{20736}$

$\Rightarrow \frac{81}{256}+\frac{256}{81}=\frac{7209m}{20736}$

$\Rightarrow \frac{6561+65536}{20736}=\frac{7209m}{20736}$

$\Rightarrow \frac{72097}{20736}=\frac{7209m}{20736}$

$\therefore m=7$

Hence, the correct answer is 7.