Multiple Choice
Estimate the square root between two consecutive whole numbers.
11. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Start by examining the expression: \(^4\sqrt{\left(-x\right)^4}\). This means the fourth root of \((-x)^4\).
Recall that the fourth root of a number is the same as raising that number to the power of \(\frac{1}{4}\). So rewrite the expression as \(\left((-x)^4\right)^{\frac{1}{4}}\).
Use the property of exponents that says \((a^m)^n = a^{m \times n}\). Apply this to get \((-x)^{4 \times \frac{1}{4}}\).
Simplify the exponent multiplication: \(4 \times \frac{1}{4} = 1\), so the expression becomes \((-x)^1\), which is just \(-x\).
However, since we are dealing with an even root (fourth root) of an even power, the result must be non-negative. Therefore, the simplified form is the absolute value of \(-x\), written as \(\left|-x\right|\).
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