Question

Evaluate $(3x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

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

Answer 1

The correct option is C

$\frac{1}{9}$

Given

$(3x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

$\because (ab{)}^m=a^m\times b^m$

$\Rightarrow$ $3^{-2}\times (x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

$\because (a^n{)}^m=(a{)}^{m\times n}$

$\Rightarrow$ $3^{-2}\times x^{4\times -2}\times (x{)}^{12\times \frac{2}{3}}$

$\Rightarrow$ $3^{-2}\times x^{-8}\times (x{)}^8$

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

$\Rightarrow$ $3^{-2}\times \frac{1}{x^8}\times (x{)}^8$

$\Rightarrow$ $3^{-2}=\frac{1}{9}$