Question

Simplify and express with positive exponents ${\left(2^{-1}÷5^{-1}\right)}^2\times {\left(\frac{-5}{8}\right)}^{-2}$

Answer 1

${(2^{-1}÷5^{-1})}^2\times {\left(\frac{-5}{8}\right)}^{-2}$

$={(\frac{1}{2}÷\frac{1}{5})}^2\times {\left(\frac{8}{-5}\right)}^2$

$={(\frac{1}{2}\times 5)}^2\times \frac{64}{25}$

$=\frac{25}{4}\times \frac{64}{25}=16$