Question

plzz solve it.........​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\bigg( \bigg( \frac{2}{3} \bigg) ^{2} \bigg)^{3} \times \bigg(\frac{2}{3} \bigg)^{ - 4} \times {3}^{ - 1} \times \frac{1}{6} =\frac{2}{81}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{\bold{Given:}}} \\ \tt: \implies \bigg[\bigg( \frac{2}{3} \bigg) ^{2} \bigg]^{3} \times \bigg( \frac{2}{3} \bigg)^{ - 4} \times {3}^{ - 1} \times \frac{1}{6} \\ \\ \red{\underline{\bold{To \: Find:}}} \\ \tt: \implies \bigg[ \bigg( \frac{2}{3} \bigg) ^{2} \bigg]^{3} \times \bigg(\frac{2}{3} \bigg)^{ - 4} \times {3}^{ - 1} \times \frac{1}{6} =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies\bigg( \bigg( \frac{2}{3} \bigg) ^{2} \bigg)^{3} \times \bigg(\frac{2}{3} \bigg)^{ - 4} \times {3}^{ - 1} \times \frac{1}{6} \\ \\ \tt \circ \: ( {x}^{m} )^{n} = {x}^{mn} \\ \\ \tt: \implies \bigg(\frac{2}{3} \bigg)^{2 \times 3} \times \bigg(\frac{2}{3} \bigg) ^{ - 4} \times \frac{1}{3} \times \frac{1}{6} \\ \\ \tt: \implies \bigg(\frac{2}{3} \bigg)^{6} \times \bigg(\frac{2}{3} \bigg) ^{ - 4} \times \frac{1}{3} \times \frac{1}{2 \times 3} \\ \\ \tt: \implies \frac{ {2}^{ 6} \times 2 {}^{ - 4} }{ {3}^{6} \times {3}^{ - 4} \times 3^{2} \times {2} } \\ \\ \tt: \implies \frac{2^{6 - 4 - 1} }{ {3}^{6 - 4 + 2} } \\ \\ \tt: \implies \frac{2}{ {3}^{4} } \\ \\ \green{\tt: \implies \frac{2}{81} } \\ \\ \tt \green{\therefore \bigg[\bigg( \frac{2}{3} \bigg) ^{2} \bigg]^{3} \times \bigg(\frac{2}{3} \bigg)^{ - 4} \times {3}^{ - 1} \times \frac{1}{6} = \frac{2}{81} }$