1. **State the problem:** Rewrite $\left(\sqrt{17}\right)^{34}$ in exponential form. 2. **Recall the rule:** The square root of a number can be written as an exponent of $\frac{1}{2}$, so $\sqrt{17} = 17^{\frac{1}{2}}$. 3. **Rewrite the expression:** $$\left(\sqrt{17}\right)^{34} = \left(17^{\frac{1}{2}}\right)^{34}$$ 4. **Use the power of a power rule:** $$\left(a^{m}\right)^{n} = a^{m \times n}$$ 5. **Calculate the exponent:** $$17^{\frac{1}{2} \times 34} = 17^{17}$$ 6. **Final answer:** $$\boxed{17^{17}}$$