Answer
$-7|x^3|$
Work Step by Step
RECALL:
(i) $\sqrt{a^2} = a$ when $a\ge0$
(ii) $\sqrt{a^2} = |a|$ when $a\lt0$
Use the rules above to obtain:
$-\sqrt{49x^6}=-\sqrt{(7x^3)^2}=-7|x^3|$
(The absolute value has to be applied to $x^3$ to make its value always nonnegative).