Question

question
simplify \\(\sqrt4{x^{32}}\\) completely given \\(x > 0\\).

Explanation:

Step1: Recall the property of radicals and exponents

The \(n\)-th root of a number \(a^m\) can be written as \(a^{\frac{m}{n}}\) when \(a\geq0\) (which is satisfied here since \(x > 0\)). So for \(\sqrt[4]{x^{32}}\), we can use the formula \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\).

Step2: Apply the formula

Here, \(n = 4\) and \(m=32\). So we have \(x^{\frac{32}{4}}\).

Step3: Simplify the exponent

Simplify \(\frac{32}{4}\), which equals \(8\). So \(x^{\frac{32}{4}}=x^{8}\).

Answer:

\(x^{8}\)