Answer
$-7$
Work Step by Step
We want to break down this problem a little to be able to work with it. The number $343$ can be broken down into a small base raised to a power: $7^3$. Let's rewrite this number:
$(-7^3)^{1/3}$
Raising a power to a power means we can multiply the two powers or exponents together:
$-7^{(3)(1/3)}$
Multiply to simplify:
$-7^{1}$
When we raise a number to the power of $1$, then the number can just be written as the base without an exponent:
$-7$
