Question

URGENT !!!
(1 supra 3 - 1)la puterea a 7-a : [0.(6)]la puterea a 5-a

Answer 1

(1/3  - 1)^7 : 0,(6)^5 = 
- (2/3)^7 : (2/3)^5 = 
-(2/3)^(7-5) = 
-(2/3)^2 =
 - 4/9 

Answer 2

$\Big(\dfrac{1}{3}-1\Big)^7 :0,(6)^5 = \\ \\ = \Big(\dfrac{-2}{3}\Big)^7:\Big(\dfrac{6}{9}\Big)^5 = \\ \\ = \Big((-1)\cdot \dfrac{2}{3}\Big)^7 :\Big(\dfrac{2}{3}\Big)^5 = \\ \\ = \left[(-1)^7\cdot \Big(\dfrac{2}{3}\Big)^7\right]:\Big(\dfrac{2}{3}\Big)^5 = \\ \\=(-1)^7\cdot \Big(\dfrac{2}{3}\Big)^7:\Big(\dfrac{2}{3}\Big)^5 \\ \\ = -\Big(\dfrac{2}{3}\Big)^{7-5} = \\ \\ = -\Big(\dfrac{2}{3}\Big)^2 = \\ \\ = -\dfrac{4}{9}$