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By what number should (-3/2)^-3 be divided so that the quotient may be (-8/27)^-2

Dear Student ,

{(\frac{- 3}{2})}^{- 3} \div x = {(\frac{- 8}{27})}^{- 2} {(\frac{- 3}{2})}^{- 3} \times \frac{1}{x} = {[{(\frac{- 2}{3})}^{3}]}^{- 2} {(\frac{- 3}{2})}^{- 3} \times \frac{1}{x} = {(\frac{- 2}{3})}^{- 6} \frac{1}{x} = {(\frac{- 2}{3})}^{- 6} \div {(\frac{- 3}{2})}^{- 3} = {(- \frac{2}{3})}^{- 6} \times {(\frac{- 2}{3})}^{3} = {(\frac{- 2}{3})}^{- 3} x = {(\frac{- 3}{2})}^{3} = \frac{- 27}{8}

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