1. The problem is to evaluate the expression $$(36x^4)^{\frac{1}{2}}$$. 2. We use the rule of exponents: $$(a^m)^n = a^{mn}$$ and the property of square roots: $$\sqrt{a} = a^{\frac{1}{2}}$$. 3. Apply the exponent to each factor inside the parentheses: $$ (36x^4)^{\frac{1}{2}} = 36^{\frac{1}{2}} \cdot (x^4)^{\frac{1}{2}} $$ 4. Simplify each term: $$ 36^{\frac{1}{2}} = \sqrt{36} = 6 $$ $$ (x^4)^{\frac{1}{2}} = x^{4 \cdot \frac{1}{2}} = x^2 $$ 5. Multiply the simplified terms: $$ 6 \cdot x^2 = 6x^2 $$ Therefore, the value of the expression is $6x^2$.