Simplify the following.
${}^4\sqrt{{(-x)}^4}$

• A. $\(\left\)|-x\(\right\)|$
• B. $2\(\left\)|-x\(\right\)|$
• C. $4\(\left\)|-x\(\right\)|$
• D. $x^2$

Answer: (A)

Verified step by step guidance

1. Start by examining the expression: \(^4\sqrt{\left(-x\right)^4}\). This means the fourth root of \((-x)^4\).
2. Recall that the fourth root and the fourth power are inverse operations, so \(^4\sqrt{a^4} = |a|\) for any real number \(a\).
3. Apply this property to the expression: \(^4\sqrt{\left(-x\right)^4} = \left| -x \right|\).
4. Use the property of absolute values that \(\left| -x \right| = |x|\), since absolute value measures distance from zero regardless of sign.
5. Therefore, the simplified form of the expression is \(|x|\).