Question

By what number should (-3/2)^-3 be divided so that quotient may be 4/27^-2​

Answer 1

Let that number be x

so,

$\frac{( { \frac{ - 3}{2} )}^{ - 3} }{x} = {( \frac{4}{27} )}^{ - 2} \\ \frac{ { (\frac{ - 2}{3} )}^{3} }{x} = ( { \frac{27}{4} )}^{2} \\ \frac{ \frac{ - 8}{27} }{x} = \frac{729}{16} \\ \frac{ - 8}{27x} = \frac{729}{16} \\ x = \frac{( - 8) \times 16}{27 \times 729} \\ x = \frac{ - 128}{19683}$