Question

Simplify:

\[\left\{ \left( \frac{2}{3} \right)^2 \right\}^3 \times \left( \frac{1}{3} \right)^{- 4} \times 3^{- 1} \times 6^{- 1}\]

Answer 1

\[\left\{ \left( \frac{2}{3} \right)^2 \right\}^3 \times \left( \frac{1}{3} \right)^{- 4} \times 3^{- 1} \times 6^{- 1}\] `=(2^2/3^2)^3xx1/(1/3)^4xx1/3xx1/6`  → ((a/b)ⁿ = aⁿ/(bⁿ)) and (a⁻ⁿ = 1/(aⁿ))

`=(4/9)^3xx1/(1/81)xx1/3xx1/6`

`=4^3/9^3xx81xx1/18`  → ((a/b)ⁿ = aⁿ/(bⁿ))

`=64/729xx81xx1/18`

`=64/9xx1/18`

`=64xx1/162`

`=64/162`

`=32/81`