Question

(1/216)^-2/3÷ (1/27)^-4/3​

Answer 1

Answer:

4/9

Step-by-step explanation:

$\frac{(\frac{1}{216})^{-2/3}}{(\frac{1}{27})^{-4/3}}$

=$\frac{(216)^{2/3}}{(27)^{4/3}}$

=$\frac{((216)^{1/3})^2}{((27)^{1/3})^2}$

=$\frac{6^2}{3^4}$

=36/81

=4/9

HOPE IT HELPS,

PLEASE THANK , FOLLOW AND MARK AS BRAINLIEST.

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{Given fractional expression,}$

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

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

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

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

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

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

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

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