Simplify the following.
${}^3\sqrt{{(-5)}^3}$

• A. $5$
• B. $-5$
• C. $-15$
• D. $15$

Answer: (B)

Verified step by step guidance

1. Identify the expression to simplify: \(^3\sqrt{\left(-5\right)^3}\), which means the cube root of \((-5)^3\).
2. Recall the property of exponents and roots: the cube root of a number raised to the third power simplifies as \(^3\sqrt{a^3} = a\) for any real number \(a\).
3. Apply this property to the expression: \(^3\sqrt{\left(-5\right)^3} = -5\) because the cube root and the cube cancel each other out.
4. Understand that since the base is negative and the root is an odd root (cube root), the result remains negative.
5. Therefore, the simplified form of the expression is \(-5\).