Question: User: what is ($\sqrt{11}$ )^3
1. **State the problem:** We need to find the value of $$\left(\sqrt{11}\right)^3$$.
2. **Recall the formula:** When raising a square root to a power, use the property $$\left(\sqrt{a}\right)^n = a^{\frac{n}{2}}$$.
3. **Apply the formula:** Here, $$a=11$$ and $$n=3$$, so:
$$\left(\sqrt{11}\right)^3 = 11^{\frac{3}{2}}$$.
4. **Rewrite the exponent:** $$11^{\frac{3}{2}} = 11^{1 + \frac{1}{2}} = 11^1 \times 11^{\frac{1}{2}} = 11 \times \sqrt{11}$$.
5. **Final answer:** $$\left(\sqrt{11}\right)^3 = 11 \sqrt{11}$$.