Question

Solve :
${\left(\frac{5^{-1}\times 7^2}{5^2\times 7^{-4}}\right)}^{-\frac{1}{3}}$ is equal to :

• A. $\frac{5}{49}$
• B. $\frac{5}{7}$
• C. $\frac{10}{49}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{49}$

${\left(\frac{5^{-1}\times 7^2}{5^2\times 7^{-4}}\right)}^{-1/3}$

$\Rightarrow (5^{-1-2}\times 7^{2-(-4)}{)}^{1/6}$

$\Rightarrow {(5^{-3}\times 7^6)}^{-1/3}$

$\Rightarrow \frac{1}{(5^{-3}\times 7^6{)}^{1/3}}$

$\Rightarrow \frac{1}{5^{-1}\times 7^2}$

$\Rightarrow \frac{5}{7^2}\Rightarrow \frac{5}{49}$