Writing Rational Exponents as Radicals

The 2 tells us the power and the 3 tells us the root.

${343}^{\frac{2}{3}}={\left(\sqrt[3]{343}\right)}^2=\sqrt[3]{{343}^2}$

We know that $\sqrt[3]{343}=7$ because $7^3=343.$ Because the cube root is easy to find, it is easiest to find the cube root before squaring for this problem. In general, it is easier to find the root first and then raise it to a power.

$${343}^{\frac{2}{3}}={\left(\sqrt[3]{343}\right)}^2=7^2=49$$