Question

Solve the following:
${\left(\frac{16}{81}\right)}^{-\frac{3}{4}}\times {\left(\frac{49}{9}\right)}^{\frac{3}{2}}+{\left(\frac{343}{216}\right)}^{\frac{2}{3}}$

Answer 1

${\left(\frac{16}{81}\right)}^{\frac{-3}{4}}\times {\left(\frac{49}{9}\right)}^{\frac{3}{2}}+{\left(\frac{343}{216}\right)}^{\frac{2}{3}}$

$={\left(\frac{2}{3}\right)}^{4\times \frac{-3}{4}}\times {\left(\frac{7}{3}\right)}^{2\times \frac{3}{2}}+{\left(\frac{7}{6}\right)}^{\frac{2}{3}\times 3}$

$={\left(\frac{2}{3}\right)}^{-3}\times {\left(\frac{7}{3}\right)}^3+{\left(\frac{7}{6}\right)}^2$

$={\left(\frac{3}{2}\right)}^2\times {\left(\frac{7}{3}\right)}^3+{\left(\frac{7}{6}\right)}^2$

$={\left(\frac{7}{2}\right)}^3+{\left(\frac{7}{6}\right)}^2$

$=\frac{343}{8}+\frac{49}{36}$

$=\frac{3185}{72}$