Question

$\text{Simplify :}{\left(\frac{7}{11}\right)}^{-3}\times {\left(\frac{11}{7}\right)}^{-3}$

Answer 1

Using properties
$a^m\times a^n=a^{m+n}\text{and}{\left(\frac{a}{b}\right)}^{-m}={\left(\frac{b}{a}\right)}^m$

We have,
${\left(\frac{7}{11}\right)}^{-3}\times {\left(\frac{11}{7}\right)}^{-3}={\left(\frac{7}{11}\right)}^{-3}\times {\left(\frac{7}{11}\right)}^3$
$={\left(\frac{7}{11}\right)}^{-3+3}={\left(\frac{7}{11}\right)}^0=1$