Question: Simplify the following expression. Assume that no radicands were formed by raising negative quantities to even powers
\u221Ax^{16}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. \u221Ax^{16} = [ ] (Simplify your answer.)
B. The root is not a real number.
Question 8, 7.1.89
1. **State the problem:** Simplify the expression $$\sqrt{x^{16}}$$ assuming the radicand is nonnegative.
2. **Recall the rule:** For any nonnegative real number $a$ and even integer $n$, $$\sqrt{a^n} = a^{\frac{n}{2}}$$.
3. **Apply the rule:** Here, $a = x$ and $n = 16$, so
$$\sqrt{x^{16}} = x^{\frac{16}{2}}$$
4. **Simplify the exponent:**
$$x^{\frac{16}{2}} = x^8$$
5. **Check the domain:** Since the problem states no negative radicands from even powers, $x^8$ is valid and real.
**Final answer:**
$$\sqrt{x^{16}} = x^8$$