simplify.\n343^{\frac{1}{3}}

Explanation:

Step1: Recall the cube - root definition

The expression $a^{\frac{1}{n}}$ is the $n$-th root of $a$. Here $n = 3$ and $a=343$, so $343^{\frac{1}{3}}=\sqrt[3]{343}$.

Step2: Find the cube - root of 343

We know that $7\times7\times7 = 343$, so $\sqrt[3]{343}=7$.

Answer:

7