Question

By what number should ${\left(\frac{2}{-5}\right)}^{-3}$ be divided so that the quotient may be ${\left(\frac{-4}{125}\right)}^{-2}$

Answer 1

${\left(\frac{2}{-5}\right)}^{-3}$ = ${\left(\frac{-5}{2}\right)}^3$

${\left(\frac{-4}{125}\right)}^{-2}$ = ${\left(\frac{125}{-4}\right)}^2$

let the number $=x$

$x\times {\left(\frac{125}{-4}\right)}^2$ = ${\left(\frac{-5}{2}\right)}^3$

$x=$${\left(\frac{-125}{8}\right)}^{}$${\left(\frac{16}{125\times 125}\right)}^{}$

$x=\frac{-2}{125}$