Question

If ${\{{\left({\left(x\right)}^5\right)}^2\times {\left(2\right)}^{-1}\}}^{\frac{1}{3}}=x^3,$ then find the value of $x$.

Answer 1

${\{{\left({\left(x\right)}^5\right)}^2\times {\left(2\right)}^{-1}\}}^{\frac{1}{3}}=x^3$

Taking cube on both the sides,
$\Rightarrow {\left\{{\{{\left({\left(x\right)}^5\right)}^2\times {\left(2\right)}^{-1}\}}^{\frac{1}{3}}\right\}}^3={\left\{x^3\right\}}^3$

$\Rightarrow \left(\right(x{)}^{10}\times \left(2{)}^{-1}\right)=x^9$
$\Rightarrow \left(\right(x{)}^{10}\times \frac{1}{2}=x^9$

$\Rightarrow (x{)}^{10}÷(x{)}^9=2$

$\Rightarrow x=2$