Question

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

• A. $\frac{-1}{9}$
• B. $\frac{1}{9}$
• C. $\frac{-1}{27}$
• D. $\frac{1}{27}$

Answer 1

The correct option is D

$\frac{1}{27}$

Given

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

$\Rightarrow$ $3^{-3}\times (x^2{)}^{-3}\times (x^9{)}^{\frac{2}{3}}$ ($\because (ab{)}^m=a^m\times b^m$)

$\Rightarrow$ $3^{-3}\times x^{2\times -3}\times (x{)}^{9\times \frac{2}{3}}$ ($\because (a^n{)}^m=(a{)}^{m\times n}$)

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

$\because a^{-m}=\frac{1}{a^m}$

$\Rightarrow$ $3^{-3}\times \frac{1}{x^6}\times (x{)}^6$

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