Question

Simplify
${\left[\frac{4}{7}\right]}^{-5}\times {\left[\frac{7}{4}\right]}^{-7}$ by giving reasons.

Answer 1

${\left(\frac{4}{7}\right)}^{-5}\times {\left(\frac{7}{4}\right)}^{-7}$

$={\left(\frac{7}{4}\right)}^5\times {\left(\frac{4}{7}\right)}^7$

$={\left(\frac{7}{4}\right)}^5\times {\left(\frac{4}{7}\right)}^5{\left(\frac{4}{7}\right)}^2$

$={\left(\frac{4}{7}\right)}^2$

$=\left(\frac{16}{49}\right)$