Answer
$-1$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a^n} = a$ when $n$ is odd
(ii) $\sqrt[n]{a^n} = |a|$ when $n$ is even
Write the number inside the radical sign as a seventh power, and then use rule (i) to obtain:
$\sqrt[7]{-1} = \sqrt[7]{(-1)^7} = -1$