REASONING Determine whether the statement √((-x)^4)=x is sometimes, always, or never true.

Name: Problem 52, Chapter 7: Algebra 2
Uploaded: 2020-03-20T21:38:34-08:00
Duration: 54 s
Channel: Chandler Austin
Description: REASONING Determine whether the statement √((-x)^4)=x is sometimes, always, or never true.

step 1 We want to determine if this statement is sometimes always or never true. So first off, this is

REASONING Determine whether the statement √((-x)^4)=x is...

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Key Concepts

Principal Even-Root Function

The principal even-root function, such as the square root or fourth root, always returns the nonnegative root of a nonnegative number. This is important because when taking an even root of an expression raised to an even power, the result is defined as the absolute value of the original expression, not the original expression itself.

Absolute Value

The absolute value represents the nonnegative magnitude of a real number regardless of its sign. In the context of simplifying expressions that involve even exponents and even roots, recognizing that the result is the absolute value helps in determining the conditions under which an equation holds true, particularly highlighting that any discrepancy arises when the original number is negative.

Even Exponents

Even exponents have the property that raising any real number to an even power results in a nonnegative value. This concept is crucial because when an expression is raised to an even power, negative and positive inputs yield the same result, which is central to understanding how the expression simplifies when later taking a root.

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