Question

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

Answer 1

Simplifying the given expression

Given,
$(3x^2{)}^{-3}\times (x^9{)}^{\frac{2}{3}}$

It can be simplified as:

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

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

$=3^{-3}\times (x{)}^{-6}\times x^6$

$=3^{-3}\times 1$

$=\frac{1}{3^3}=\frac{1}{27}$

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