1. The problem is to simplify the expression involving powers of $x$: $$x^{\frac{5}{3}} \div x^2$$. 2. Recall the rule for dividing powers with the same base: $$x^a \div x^b = x^{a-b}$$. 3. Apply this rule to the given expression: $$x^{\frac{5}{3}} \div x^2 = x^{\frac{5}{3} - 2}$$. 4. Convert the integer 2 to a fraction with denominator 3 to subtract easily: $$2 = \frac{6}{3}$$. 5. Substitute and subtract the exponents: $$x^{\frac{5}{3} - \frac{6}{3}} = x^{\frac{5-6}{3}} = x^{-\frac{1}{3}}$$. 6. The simplified form is $$x^{-\frac{1}{3}}$$, which means the reciprocal of the cube root of $x$. This shows how to subtract exponents when dividing powers with the same base, converting integers to fractions for easy subtraction.