Question

simplify.
\\( \sqrt{x^{22}} \\)
assume that the variable represents a positive real number.

Explanation:

Step1: Recall the property of square roots

For a non - negative real number \(a\) and positive integer \(n\), \(\sqrt{a^{n}}=a^{\frac{n}{2}}\) when \(n\) is even (since the variable \(x\) represents a positive real number, we don't have to worry about the domain restrictions for the square root to be real in terms of the sign of \(x\)). Here, \(a = x\) and \(n = 22\).

Step2: Apply the formula

We have \(\sqrt{x^{22}}=x^{\frac{22}{2}}\)

Step3: Simplify the exponent

Simplify \(\frac{22}{2}=11\), so \(x^{\frac{22}{2}}=x^{11}\)

Answer:

\(x^{11}\)