Question

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

Answer 1

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

$=3^{-3}\times x^{-5}\times x^6$ using ${\left(a^n\right)}^m=a^{nm}$

$=3^{-3}\times x^{-5+6}$ using $a^m\times a^n=a^{m+n}$

$=\frac{1}{3^3}x$ using $a^{-m}=\frac{1}{a^m}$

$a=\frac{x}{27}$

$\therefore {\left(3x^2\right)}^{-3}\times {\left(x^9\right)}^{\frac{2}{3}}=\frac{x}{27}$