Question

Evaluate : ${\left(\frac{-4}{5}\right)}^{-10}\times {\left(\frac{-4}{5}\right)}^{15}÷{\left(\frac{-4}{5}\right)}^8$

Answer 1

$(\frac{-4}{5}{)}^{-10}\times (\frac{-4}{5}{)}^{15}÷(\frac{-4}{5}{)}^8$

$=(\frac{-4}{5}{)}^{-10+15}÷(\frac{-4}{5}{)}^8$

$=(\frac{-4}{5}{)}^5÷(\frac{-4}{5}{)}^8$

$=(\frac{-4}{5}{)}^{5-8}$

$=(\frac{-4}{5}{)}^{-3}$

$(-4{)}^{-3}\times \frac{1}{(5{)}^3}$

$\frac{1}{(-4{)}^3}\times (5{)}^3$

$=\frac{125}{64}$