Simplify the root.
${-}^4\sqrt{10,000}$

• A. $-10$
• B. $10$
• C. $0.1$
• D. $-100$

Answer: (A)

Verified step by step guidance

1. Identify the expression to simplify: \(-^4\sqrt{10,000}\), which means the negative of the fourth root of 10,000.
2. Rewrite 10,000 as a power of 10 to make it easier to work with roots. Since \(10,000 = 10^4\), substitute this into the expression.
3. Apply the property of radicals that \(\sqrt[n]{a^m} = a^{\frac{m}{n}}\). Here, the fourth root of \$10^4$ is \(10^{\frac{4}{4}}\).
4. Simplify the exponent: \(10^{\frac{4}{4}} = 10^1 = 10\).
5. Don't forget the negative sign outside the root, so the simplified expression is \(-10\).