Question

simplify.
\sqrt{w^{12}}
assume that the variable represents a

Explanation:

Step1: Recall the square root property

For a non - negative real number \(a\) and positive integer \(n\), \(\sqrt{x^{n}}=x^{\frac{n}{2}}\) when \(x\geq0\). Here we have \(\sqrt{w^{12}}\), and we can apply the property of exponents for square roots.

Step2: Apply the exponent rule

Using the formula \(\sqrt{x^{n}} = x^{\frac{n}{2}}\), where \(x = w\) and \(n = 12\). So we calculate \(\frac{12}{2}=6\). Then \(\sqrt{w^{12}}=w^{6}\) (since we assume the variable represents a non - negative real number, we don't have to consider the absolute value in this case as \(w^{6}\) is non - negative for all real \(w\)).

Answer:

\(w^{6}\)