Question

question
simplify \\(\sqrt{x^8}\\) completely given \\(x > 0\\).

Explanation:

Step1: Recall the property of square roots and exponents

The square root of a number \( a^n \) (where \( a\geq0 \)) can be simplified using the rule \( \sqrt{a^n}=a^{\frac{n}{2}} \) when \( n \) is even. Here, we have \( \sqrt{x^8} \) with \( x > 0 \), so we can apply this rule.

Step2: Apply the exponent rule

Using the rule \( \sqrt{x^8}=x^{\frac{8}{2}} \)

Step3: Simplify the exponent

Simplify \( \frac{8}{2}=4 \), so \( x^{\frac{8}{2}} = x^4 \)

Answer:

\( x^4 \)