Question

What number should ${\left(\frac{-1}{5}\right)}^{-1}$ be multiplied so that the product may be equal to ${\left(\frac{-1}{5}\right)}^{-3}$

Answer 1

${\left(\frac{-1}{5}\right)}^{-1}\times x={\left(\frac{-1}{5}\right)}^{-3}\Rightarrow x=\frac{{\left(\frac{-1}{5}\right)}^{-3}}{{\left(\frac{-1}{5}\right)}^{-1}}=\frac{{\left(\frac{-1}{5}\right)}^{-3}}{(-1{)}^1{\left(\frac{-1}{5}\right)}^{-1}}=-{\left(\frac{-1}{5}\right)}^{-3+1}\Rightarrow x=-{\left(\frac{-1}{5}\right)}^{-2}=-(5{)}^2=-25$
It should be multiplied by -25 or ${\left(\frac{-1}{5}\right)}^{-2}$