1. We are asked to find the real solution(s) of the equation $$\frac{1}{3} x^4 = 27$$. 2. The equation involves a quartic term $x^4$. To solve for $x$, we first isolate $x^4$ by multiplying both sides by 3: $$x^4 = 27 \times 3$$ 3. Simplify the right side: $$x^4 = 81$$ 4. To solve for $x$, take the fourth root of both sides. Remember, the fourth root of a positive number has two real solutions: one positive and one negative: $$x = \pm \sqrt[4]{81}$$ 5. Since $81 = 3^4$, we have: $$x = \pm 3$$ 6. Therefore, the real solutions to the equation are: $$x = 3 \text{ and } x = -3$$