Question

find fourth root of (36)^-2​

Answer 1

Answer:

$\sf \sqrt[4]{{36}^{-2}}= 0. \overline{11}$

$\sf We \: will \: convert \: 0. \overline{11} \: into \: fraction \: to \: get \: accurate \: value$

$\sf Let \: x = 0. \overline{11}.....(1)$

$\sf Then \: 10x= 1. \overline{11}.......(2)$

$\sf Subtracting \: (1) \: from \: (2), \\ \\ 10x-x = 1. \overline{11}- 0. \overline{11}$

$\sf 9x=1$

$\sf x= \dfrac{1}{9}$

$\therefore \sf 4th \: root \: of \: {36}^{-2} = \dfrac{1}{9}$

hope it helps

Answer 2

Answer:

1/6

Step-by-step explanation:

(36)^-2=1/(36)^2

=1/1296

Fourth root of 1/1296=1/6

[As 6×6×6×6=1296]

HOPE IT HELPS