Multiple Choice
Simplify the following.
11. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Identify the expression to simplify: \(^7\sqrt{\left(-x-1\right)^7}\). This means the 7th root of \(\left(-x-1\right)^7\).
Recall the property of radicals and exponents: \(\sqrt[n]{a^n} = |a|\) if \(n\) is even, and \(\sqrt[n]{a^n} = a\) if \(n\) is odd. Since 7 is odd, the 7th root of \(a^7\) simplifies directly to \(a\).
Apply this property to the expression: \(^7\sqrt{\left(-x-1\right)^7} = -x - 1\).
Note that the expression \(7\left(-x-1\right)\) is a separate expression and does not affect the simplification of the radical.
Therefore, the simplified form of the original expression is \(-x - 1\).
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