Solve the Nested Expression: -|-x³| Step by Step

Absolute Value with Negative Sign Outside

−∣−x3∣= -\left|-x^3\right|=

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Step-by-step written solution

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1

Understand the problem

−∣−x3∣= -\left|-x^3\right|=

2

Step-by-step solution

The expression has an absolute value and a negative sign outside of the absolute value. When you take the absolute value of −x3 -x^3 , it results in ∣x3∣ |x^3| , which is x3 x^3 assumingx x is a real number. The negative sign outside the absolute value inverts it back to −x3 -x^3 . Thus, the correct interpretation of the original expression −∣−x3∣ -\left|-x^3\right| is −x3 -x^3 .

3

Final Answer

−x3 -x^3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Absolute value always gives non-negative result first
  • Technique: ∣−x3∣=∣x3∣=x3 |-x^3| = |x^3| = x^3 for real x
  • Check: Apply outer negative: −∣x3∣=−x3 -|x^3| = -x^3 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the negative sign outside the absolute value
    Don't think −∣−x3∣ -|-x^3| equals x3 x^3 ! Students often forget the negative sign outside affects the final result. Always apply the outside negative sign after finding the absolute value.

Practice Quiz

Test your knowledge with interactive questions

Determine the absolute value of the following number:

\( \left|18\right|= \)

FAQ

Everything you need to know about this question

Why does ∣−x3∣ |-x^3| equal ∣x3∣ |x^3| ?

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For real numbers, absolute value removes negative signs. Since −x3 -x^3 and x3 x^3 have the same absolute value, ∣−x3∣=∣x3∣ |-x^3| = |x^3| .

What's the difference between the inner and outer negative signs?

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The inner negative (in −x3 -x^3 ) gets removed by absolute value. The outer negative (before the absolute value bars) stays and affects the final answer!

Does the order matter when I have multiple operations?

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Yes! Always work from inside out: first find ∣−x3∣ |-x^3| , then apply the outer negative sign to get your final answer.

Will this always give me −x3 -x^3 as the answer?

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For real numbers, yes! The expression −∣−x3∣ -|-x^3| will always simplify to −x3 -x^3 regardless of whether x is positive or negative.

How can I check if my answer is correct?

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Try specific values! If x = 2, then −∣−23∣=−∣−8∣=−8 -|-2^3| = -|-8| = -8 , and −x3=−23=−8 -x^3 = -2^3 = -8 . They match! ✓

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