1. **State the problem:** Simplify the expression $$v^{\frac{11}{4}} \cdot v^{\frac{1}{4}}$$ assuming all variables are positive. 2. **Recall the rule for multiplying powers with the same base:** When multiplying expressions with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule:** $$v^{\frac{11}{4}} \cdot v^{\frac{1}{4}} = v^{\frac{11}{4} + \frac{1}{4}}$$ 4. **Add the exponents:** $$\frac{11}{4} + \frac{1}{4} = \frac{11 + 1}{4} = \frac{12}{4}$$ 5. **Simplify the fraction:** $$\frac{12}{4} = \cancel{\frac{12}{4}}^{3}$$ 6. **Final simplified expression:** $$v^3$$ **Answer:** $v^3$