Simplify the following.
${}^4\sqrt{{(2-a)}^4}$

• A. $4\mid 2-a\mid$
• B. ${(2-a)}^2$
• C. ${(2-a)}^4$
• D. $\mid 2-a\mid$

Answer: (D)

Verified step by step guidance

1. Recognize that the expression is the fourth root of \( (2 - a)^4 \), which can be written as \( \sqrt[4]{(2 - a)^4} \).
2. Recall the property of radicals and exponents: \( \sqrt[n]{x^n} = |x| \) when \(n\) is even, because the root of an even power returns the absolute value of the base.
3. Apply this property to simplify \( \sqrt[4]{(2 - a)^4} \) to \( |2 - a| \).
4. Understand that the absolute value is necessary because raising to an even power removes any negative sign, so the root must return a non-negative value.
5. Conclude that the simplified form of the expression is \( |2 - a| \).