Simplify the root.
${-}^5\sqrt{1024}$

• A. $4$
• B. $-4$
• C. $0.16$
• D. $-160$

Answer: (B)

Verified step by step guidance

1. Identify the expression to simplify: \(-^5\sqrt{1024}\). This means the negative of the 5th root of 1024.
2. Recall that the 5th root of a number \(a\) is a value \(x\) such that \(x^5 = a\). So, we need to find \(x\) where \(x^5 = 1024\).
3. Express 1024 as a power of a smaller number if possible. For example, recognize that \$1024 = 2^{10}$.
4. Rewrite the 5th root using exponents: \(^5\sqrt{1024} = 1024^{\frac{1}{5}} = (2^{10})^{\frac{1}{5}}\).
5. Use the power of a power rule: \((2^{10})^{\frac{1}{5}} = 2^{10 \times \frac{1}{5}} = 2^2\). Then apply the negative sign outside the root to get the final simplified expression.