Question

Simplify: $\frac{1}{{\left(3x^2\right)}^{-3}\times {\left(x^9\right)}^{\frac{2}{3}}}$

Answer 1

We have,

${\left(3x^2\right)}^{-3}\times {\left(x^9\right)}^{\frac{2}{3}}$

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

$=\frac{1}{(3^3\times x^6)}\times {\left(x^3\right)}^2$

$=\frac{1}{(27\times x^6)}\times \left(x^6\right)$

$=\frac{1}{27}$

Hence, the value is $\frac{1}{27}$.