1. **State the problem:** Simplify the expression $\sqrt{8^6}$. 2. **Recall the formula:** The square root of a number $x$ is $\sqrt{x} = x^{\frac{1}{2}}$. 3. **Rewrite the expression using exponents:** $$\sqrt{8^6} = (8^6)^{\frac{1}{2}}$$ 4. **Use the power of a power rule:** $$(a^m)^n = a^{m \times n}$$ 5. **Apply the rule:** $$(8^6)^{\frac{1}{2}} = 8^{6 \times \frac{1}{2}} = 8^3$$ 6. **Express 8 as a power of 2:** $$8 = 2^3$$ 7. **Substitute:** $$8^3 = (2^3)^3$$ 8. **Use the power of a power rule again:** $$(2^3)^3 = 2^{3 \times 3} = 2^9$$ 9. **Final answer:** $$\sqrt{8^6} = 2^9$$ Therefore, the correct choice is **B 2^9**.