Question

Simplify ${\left(\frac{-3}{4}\right)}^{-5}+{\left(\frac{-3}{4}\right)}^{-3}$

Answer 1

${\left(\frac{-3}{4}\right)}^{-5}+{\left(\frac{-3}{4}\right)}^{-3}$
$={\left(\frac{-3}{4}\right)}^{-3}[{\left(\frac{-3}{4}\right)}^{-2}+1]$
$={\left(\frac{-4}{3}\right)}^3[{\left(\frac{-4}{3}\right)}^2+1]$
$=-\left(\frac{64}{27}\right)[\left(\frac{16}{9}\right)+1]$
$=-\left(\frac{64}{27}\right)\left[\left(\frac{16+9}{9}\right)\right]$
$=-\left(\frac{64}{27}\right)\left(\frac{25}{9}\right)$