Question

The value of $\frac{{\left(81\right)}^{1/3}\times {\left(576\right)}^{1/3}}{{64}^{2/3}\times {\left(27\right)}^{2/3}}$ is

Answer 1

Given,

$\frac{(81{)}^{1/3}\times (576{)}^{1/3}}{(64{)}^{2/3}\times (27{)}^{2/3}}$

$\Rightarrow \frac{(3\times 3^3{)}^{1/3}\times ({24}^2{)}^{1/3}}{(4^3{)}^{2/3}\times (3^3{)}^{2/3}}$

$\Rightarrow \frac{(3\times 3^3{)}^{1/3}\times (3\times 8{)}^{2/3}}{(4{)}^2\times 3^2}$

$\Rightarrow \frac{(3^{1/3}\times 3)\times (3^{2/3}\times 2^2)}{(4{)}^2\times 3^2}$

$\Rightarrow \frac{(3\times 3)\times 2^2}{(4{)}^2\times 3^2}$

$\Rightarrow \frac{1}{4}$

Hence, this is the answer.