Question: Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.
$\sqrt{a^{14}}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\sqrt{a^{14}} = $ [ ] (Simplify your answer.)
B. The square root cannot be simplified to a real number.
1. **State the problem:** Simplify the expression $$\sqrt{a^{14}}$$ and use absolute value notation if necessary.
2. **Recall the rule:** The square root of a power can be simplified using $$\sqrt{x^n} = |x|^{\frac{n}{2}}$$ when $n$ is even, to ensure the result is non-negative.
3. **Apply the rule:**
$$\sqrt{a^{14}} = |a|^{\frac{14}{2}} = |a|^7$$
4. **Interpretation:** Since the square root function outputs the principal (non-negative) root, we use absolute value to ensure the expression is valid for all real $a$.
5. **Final answer:**
$$\boxed{\sqrt{a^{14}} = |a|^7}$$