Solve: Finding -|5³| Using Order of Operations

Q: Why isn't the answer positive 125 if absolute value makes everything positive?

Great question! The absolute value $ |5^3| = 125 $ is positive, but there's a negative sign outside the absolute value bars. So $ -|5^3| = -125 $.

Q: What's the difference between -|5³| and |-5³|?

Big difference! $ -|5^3| = -125 $ (negative outside), but $ |-5^3| = |-125| = 125 $ (negative inside). The position of the negative sign matters!

Q: Do I calculate the exponent first or the absolute value first?

Always follow order of operations! First calculate the exponent: $ 5^3 = 125 $. Then apply absolute value: $ |125| = 125 $. Finally the negative: $ -125 $.

Q: Can absolute value ever give a negative result?

No! Absolute value itself is always positive or zero. However, if there's a negative sign outside the absolute value (like $ -|x| $), then the final result will be negative.

Q: How can I remember when the answer should be negative?

Look for the negative sign's position! If it's outside the absolute value bars (like $ -|\text{something}| $), your final answer will be negative. If it's inside, the absolute value makes it positive.

Order of Operations with Negative Absolute Values

$-\lvert5^3\rvert=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-\lvert5^3\rvert=$

Step-by-step solution

First, calculate the cube of 5: $5^3 = 125$ .

Then, apply the absolute value:
since 125 is positive, $\lvert 125 \rvert = 125$ .

Finally, apply the negative sign outside the absolute value: $-\lvert 125 \rvert = -125$ .

Final Answer

$-125$

Key Points to Remember

Essential concepts to master this topic

Rule: Absolute value bars act as grouping symbols requiring evaluation first
Technique: Calculate $5^3 = 125$ , then $|125| = 125$ , finally $-125$
Check: Negative sign outside absolute value means answer is negative: $-|5^3| = -125$ ✓

Common Mistakes

Avoid these frequent errors

Applying negative sign before calculating absolute value
Don't calculate $|-5^3| = |-125| = 125$ ! The negative is outside the absolute value bars, not inside. Always evaluate what's inside the absolute value first, then apply the negative sign to the result.

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 isn't the answer positive 125 if absolute value makes everything positive?

Great question! The absolute value $|5^3| = 125$ is positive, but there's a negative sign outside the absolute value bars. So $-|5^3| = -125$ .

What's the difference between -|5³| and |-5³|?

Big difference! $-|5^3| = -125$ (negative outside), but $|-5^3| = |-125| = 125$ (negative inside). The position of the negative sign matters!

Do I calculate the exponent first or the absolute value first?

Always follow order of operations! First calculate the exponent: $5^3 = 125$ . Then apply absolute value: $|125| = 125$ . Finally the negative: $-125$ .

Can absolute value ever give a negative result?

No! Absolute value itself is always positive or zero. However, if there's a negative sign outside the absolute value (like $-|x|$ ), then the final result will be negative.

How can I remember when the answer should be negative?

Look for the negative sign's position! If it's outside the absolute value bars (like $-|\text{something}|$ ), your final answer will be negative. If it's inside, the absolute value makes it positive.

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