stmt1,

sqrt(x^4)=9

-->x^4=81

But x can be 3 or -3.

Insuff

stmt2,

sqrt(x^2)=-x

-->x<0.but we don't know value of x

Insuff

Combining 1 and 2

Since x<0 x=-3

Pick C

Hi!

(1)
√(x^4) = 9
(x^4)^0.5 = 9
x^(4*0.5) = 9
x^2 = 9
either x = -3 or x = 3
Statement (1) ALONE is INSUFFICIENT
We should eliminate answers A and D

(2)
√(x^2) = -x
|x| = -x
|x| must be greater than 0
either x < 0 or x = 0
Statement (2) ALONE is INSUFFICIENT
We should eliminate answer B

(1) & (2)
x^2 = 9 & |x| = -x
(either x = -3 or x = 3) & (either x < 0 or x = 0)
Therefore, x = -3
We should eliminate answer E and choose answer C
Statements (1) and (2) both are TOGETHER SUFFICIENT

Hope it helps!
Best,
Maciek

Thanks a lot guys, I got it now....