Question

simplify the radical expression.
\\(sqrt{x^{14}}\\)
write your answer in the form \\(a\\), \\(sqrt{b}\\), or \\(asqrt{b}\\), where \\(a\\) and \\(b\\) are constants or expressions in \\(x\\). use at most one radical in your answer, and at most one absolute value symbol in your expression for \\(a\\).

Explanation:

Step1: Rewrite radical as exponent

$\sqrt{x^{14}} = (x^{14})^{\frac{1}{2}}$

Step2: Apply exponent power rule

$(x^{14})^{\frac{1}{2}} = x^{14 \times \frac{1}{2}} = x^7$

Step3: Account for absolute value

Since square root gives non-negative result, $|x^7|$

Answer:

$|x^7|$