Question

(1/216)-3/2/(1/27)-2/3

Answer 1

(1/216)-3/2(1/27)-2/3
= 1/216-3/54-2/3
= (1-12-144)/216
= (1-156)/216
= -155/216

Answer 2

$\bf \underline{Solution-}$

$\textsf{Given fractional expression,}$

$\sf{ \bigg( \frac{1}{216} \bigg) ^{ - \frac{2}{3} } \div \bigg( \frac{1}{27} \bigg)^{ - \frac{4}{3} } }$

$\sf{ \Rightarrow \: (216 {)}^{ \frac{2}{3} } \div (27 {)}^{ \frac{4}{3} } }$

$\sf{ \Rightarrow \: ( {6}^{3} {)}^{ \frac{2}{3} } \div ( {3}^{3} {)}^{ \frac{4}{3} } }$

$\sf{ \Rightarrow \: {6}^{ \cancel3 \times \frac{2}{ \cancel3} } \div {3}^{ \cancel3 \times \frac{4}{ \cancel3} } }$

$\sf{ \Rightarrow \: {6}^{2} \div {3}^{4} }$

$\sf{ \Rightarrow \: 6 \times 6 \div 3 \times 3 \times 3 \times 3}$

$\sf{ \Rightarrow \: 36 \div 81}$

$\sf{ \Rightarrow \: \frac{36}{81} }$