1. We are given the expression $\sqrt[3]{\frac{81}{3}}$ and need to write it in the form $3^k$ and find $k$. 2. Simplify the fraction inside the cube root: $$\frac{81}{3} = 27$$ 3. So the expression becomes: $$\sqrt[3]{27}$$ 4. Recall that $27 = 3^3$, so: $$\sqrt[3]{3^3}$$ 5. The cube root of $3^3$ is: $$3^{3 \times \frac{1}{3}} = 3^1 = 3$$ 6. Therefore, the expression can be written as $3^k$ where: $$k = 1$$