Question

The simplified form of $[{\left(\frac{3}{7}\right)}^5\times {\left(\frac{3}{7}\right)}^2]÷{\left(\frac{343}{27}\right)}^3$ is ${\frac{m}{7}}^{16}$. The value of $m$ is

Answer 1

$[{\left(\frac{3}{7}\right)}^5\times {\left(\frac{3}{7}\right)}^2]÷{\left(\frac{343}{27}\right)}^3$

$={\left(\frac{3}{7}\right)}^{5+2}÷{\left(\frac{7^3}{3^3}\right)}^3$

$={\left(\frac{3}{7}\right)}^7÷{\left\{{\left(\frac{7}{3}\right)}^3\right\}}^3$

$={\left(\frac{3}{7}\right)}^7\times {\left(\frac{3}{7}\right)}^9$

$={\left(\frac{3}{7}\right)}^{7+9}={\left(\frac{3}{7}\right)}^{16}$