Question

By what number should ${\left(\frac{3}{4}\right)}^{-3}$ be divided so that the quotient becomes 128?

Answer 1

Let the number be $x$
${\left(\frac{3}{4}\right)}^{-3}÷x=128$
$=>x=\frac{(\frac{3}{4}{)}^{-3}}{128}$
$=>x=\frac{(\frac{4}{3}{)}^3}{128}$
$=>x=\frac{4^3}{3^3\times 128}$
$=>x=\frac{64}{27\times 128}$
$=>x=\frac{1}{27\times 2}$
$=>x=\frac{1}{54}$