Answer
True
Work Step by Step
The definition of rational exponents states that $x^\frac{m}{n}=\sqrt[n] {x^m}$. We use this to rewrite each of the radicals in rational exponent form: $\frac{7^\frac{1}{2}}{7^\frac{1}{3}}=7^\frac{1}{6}$
To divide powers with the same base, we subtract the exponents. We use this rule to simplify the left side of the equation: $7^{\frac{1}{2}-\frac{1}{3}}=7^{\frac{1}{6}}$
Since $7^{\frac{1}{6}}=7^{\frac{1}{6}}$, the expressions are equivalent.
