Question

Find the value of $(\frac{1}{3^3}{)}^{\frac{1}{7}}$.

• A. $3^{\frac{-2}{7}}$
• B. $3^{\frac{-3}{7}}$
• C. $3^{\frac{-3}{7}}$
• D. None of the above

Answer 1

The correct option is C $3^{\frac{-3}{7}}$

$(\frac{1}{3^3}{)}^{\frac{1}{7}}$
$\because \frac{1}{a^m}=a^{-m}$
$\Rightarrow (\frac{1}{3^3}{)}^{\frac{1}{7}}=(3^{-3}{)}^{\frac{1}{7}}$
$\because (a^m{)}^n=a^{mn}$
$\Rightarrow 3^{(-3\times \frac{1}{7})}$
$=3^{\frac{-3}{7}}$