Question

Solve the following :
$\left(i\right){\left(\frac{27}{125}\right)}^{\frac{2}{3}}\times {\left(\frac{9}{25}\right)}^{-\frac{3}{2}}$
$\left(ii\right)7^0\times {\left(25\right)}^{-\frac{3}{2}}-5^{-3}$
$\left(iii\right){\left(\frac{16}{81}\right)}^{-\frac{3}{4}}\times {\left(\frac{49}{9}\right)}^{\frac{3}{2}}÷{\left(\frac{343}{216}\right)}^{\frac{2}{3}}$

Answer 1

$\left(i\right){\left(\frac{27}{125}\right)}^{\frac{2}{3}}\times {\left(\frac{9}{25}\right)}^{\frac{3}{2}}$

${\left({\left(\frac{3}{5}\right)}^3\right)}^{\frac{2}{3}}\times {\left(\frac{3}{5}\right)}^{\frac{-3}{2}}$

${\left(\frac{3}{5}\right)}^2\times {\left(\frac{3}{5}\right)}^{-3}=\frac{3^2}{5^2}\times \frac{5^3}{3^3}=\frac{5}{3}$

$\left(ii\right)7^o\times (25{)}^{\frac{-3}{2}}-5^{-3}$

$1\times (5^2{)}^{-3/2}\times {\left(\frac{49}{9}\right)}^{3/2}÷{\left(\frac{343}{216}\right)}^{\frac{2}{3}}$

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

$\frac{2^{-3}}{3^{-3}}\times \frac{7^3}{3^3}\times \frac{3^2}{7^2}=7\times 2^2\times 3^2\times 2^3=\frac{9\times 9}{2}=\frac{63}{2}$