Question

evaluate:-

Please answer this question it's urgent​

Answer 1

Answer:

0.395

Step-by-step explanation:

= [(2/3)^3]^2 * (1/3)^-4 *9^-1 (1/2)^1

= (2/3)^6* (1/3)^-4 *(3)^-2 (1/2)^1                                ∵ [(a^m)^n = (a)^m+n]

= (2/3)^6* (1/3)^-4 *(3)^2 (1/2)                                    ∵  [(a)^-m = (1/a)^m ]

= 2/3 * 2/3 * 2/3 * 2/3 * 2/3 * 2/3 * 3 * 3 * 1/2    

= 32/81

= 0.395  

Answer 2

Solution

we have

$\sf : \implies \: \bigg[ \bigg( \dfrac{2}{3} \bigg)^{3} \bigg]^{2} \times \bigg( \dfrac{1}{3} \bigg)^{ - 4} \times {9}^{ - 1} \times \bigg( \dfrac{1}{2} \bigg)^{1}$

We use exponential identities

$\sf : \implies \: (a {}^{m} )^{n} = {a}^{mn}$

$\sf : \implies \: {a}^{ - 1} = \dfrac{1}{a}$

$\sf : \implies \: \bigg( \dfrac{1}{a} \bigg)^{ - m} = {a}^{m}$

Now Use this identities

$\sf : \implies \: \bigg[ \bigg( \dfrac{2}{3} \bigg)^{3} \bigg]^{2} \times \bigg( \dfrac{1}{3} \bigg)^{ - 4} \times {9}^{ - 1} \times \bigg( \dfrac{1}{2} \bigg)^{1}$

$\sf : \implies \: \bigg( \dfrac{2}{3} \bigg)^{6} \times (3) ^{4} \times \dfrac{1}{9} \times \dfrac{1}{2}$

$\sf : \implies \: \bigg( \dfrac{2}{3} \bigg)^{6} \times {3}^{4} \times \dfrac{1}{ {3}^{2} } \times \dfrac{1}{2}$

$\sf : \implies \: \dfrac{ {2}^{6} }{ {3}^{6} } \times {3}^{2} \times \dfrac{1}{2}$

$\sf : \implies \: \dfrac{2 {}^{5} }{ {3}^{4} }$

$\sf : \implies \dfrac{2 \times 2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3}$

$\sf : \implies \: \dfrac{32}{81}$

Answer

$\sf : \implies \: \dfrac{32}{81}$