Question

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

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

Answer 1

The correct option is D

$\frac{1}{9}$

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

$=3^{-2}\times (x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$
$[\because (ab{)}^m=a^m\times b^m]$

$=3^{-2}\times x^{4\times -2}\times (x{)}^{12\times \frac{2}{3}}$
$[\because (a^n{)}^m=\left(a{)}^{m\times n}\right]$

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

$=3^{-2}\times \frac{1}{x^8}\times (x{)}^8$ $[\because a^{-m}=\frac{1}{a^m}]$

$=3^{-2}$

$=\frac{1}{3^2}$ $[\because a^{-m}=\frac{1}{a^m}]$

$=\frac{1}{9}$