Discussion

Question:

Simplify: ${[{(\frac{2}{3})}^{2}]}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times \frac{1}{6}$

Explanation:

Given, ${[{(\frac{2}{3})}^{2}]}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times \frac{1}{6}$

= ${(\frac{2}{3})}^{2 \times 3} \times 3^{4} \times \frac{1}{3} \times \frac{1}{6}$

= $\frac{2^{6}}{3^{6}} \times 3^{4} \times \frac{1}{3} \times \frac{1}{2 \times 3}$

= $\frac{2^{5}}{3^{4}}$ = $\frac{32}{81}$

Hence, option (b).

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