Question

question
simplify \\(\sqrt{x^{12}}\\) completely given \\(x > 0\\).
answer attempt 1 out of 2

Explanation:

Step1: Recall the square root property

For a non - negative real number \(a\) and positive integer \(n\), \(\sqrt{a^{m}}=a^{\frac{m}{2}}\) when \(m\) is even (since \(x>0\), we don't have to worry about the sign of the root here). In the expression \(\sqrt{x^{12}}\), we can apply the rule \(\sqrt{a^{m}}=a^{\frac{m}{2}}\) where \(a = x\) and \(m = 12\).
So, \(\sqrt{x^{12}}=x^{\frac{12}{2}}\)

Step2: Simplify the exponent

Simplify the fraction \(\frac{12}{2}\). \(\frac{12}{2}=6\). So \(x^{\frac{12}{2}}=x^{6}\)

Answer:

\(x^{6}\)