1. **State the problem:** Evaluate the expression $$ (36x^4)^{\frac{1}{2}} $$. 2. **Recall the rule:** The square root of a product is the product of the square roots, and the power of a power rule states $$ (a^m)^n = a^{mn} $$. 3. **Apply the power to each factor:** $$ (36x^4)^{\frac{1}{2}} = 36^{\frac{1}{2}} \times (x^4)^{\frac{1}{2}} $$ 4. **Simplify each term:** - $$ 36^{\frac{1}{2}} = \sqrt{36} = 6 $$ - $$ (x^4)^{\frac{1}{2}} = x^{4 \times \frac{1}{2}} = x^2 $$ 5. **Combine the results:** $$ 6 \times x^2 = 6x^2 $$ **Final answer:** $$ 6x^2 $$