1. The problem asks which student correctly solved the expression $$x^{\frac{1}{3}} \cdot x^{\frac{1}{4}}$$. 2. The rule for multiplying powers with the same base is to add the exponents: $$a^m \cdot a^n = a^{m+n}$$. 3. Applying this rule, we add the exponents $$\frac{1}{3} + \frac{1}{4}$$. 4. Find a common denominator for $$\frac{1}{3}$$ and $$\frac{1}{4}$$, which is 12. 5. Convert the fractions: $$\frac{1}{3} = \frac{4}{12}$$ and $$\frac{1}{4} = \frac{3}{12}$$. 6. Add the fractions: $$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$. 7. So, $$x^{\frac{1}{3}} \cdot x^{\frac{1}{4}} = x^{\frac{7}{12}}$$. 8. Checking the students' answers: - Jo says $$x^{\frac{7}{12}}$$ because exponents should be added (correct). - Kerrie says $$x^{\frac{2}{7}}$$ (incorrect addition). - Alex says $$x^{\frac{7}{12}}$$ because exponents should be multiplied (incorrect reasoning). - Tracy says $$x^{\frac{1}{12}}$$ because exponents should be multiplied (incorrect). Final answer: Jo correctly solved the expression.