Solve the Absolute Value Expression: |2³ - 5|

Q: Why can't I take the absolute value of each term separately?

Absolute value bars act like grouping symbols - you must complete everything inside them first! Taking $ |2^3| - |5| $ changes the mathematical meaning and can lead to wrong answers.

Q: How do I know when to use absolute value?

Look for the vertical bars $ | | $ around an expression. These bars mean "find the distance from zero" - always a positive result!

Q: Can the answer ever be negative?

Never! Absolute value always gives a non-negative result. If you get a negative answer, check your work - you likely made an error in the order of operations.

Q: What's the difference between this and regular parentheses?

Both require you to work inside first, but absolute value bars have an extra step: after completing internal operations, you must make the result non-negative (positive or zero).

Absolute Value with Order of Operations

$\left|2^3 - 5\right| =$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\left|2^3 - 5\right| =$

Step-by-step solution

The expression $\left|2^3 - 5\right|$ represents the absolute value of the result of subtracting 5 from $2^3$ .

Calculate the power: $2^3 = 8$ .

Subtract the numbers: $8 - 5 = 3$ .

The absolute value of 3 is $3$ , so the answer is $3$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Always complete operations inside absolute value bars first
Technique: Calculate $2^3 = 8$ , then $8 - 5 = 3$ , then $|3| = 3$
Check: Verify that $|2^3 - 5| = |8 - 5| = |3| = 3$ ✓

Common Mistakes

Avoid these frequent errors

Finding absolute value before completing internal operations
Don't calculate $|2^3| - |5| = 8 - 5 = 3$ ! This breaks the order of operations and can give wrong results when dealing with negative values inside absolute value bars. Always complete all operations inside the absolute value bars first, then apply 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 can't I take the absolute value of each term separately?

Absolute value bars act like grouping symbols - you must complete everything inside them first! Taking $|2^3| - |5|$ changes the mathematical meaning and can lead to wrong answers.

What if the result inside the absolute value bars is negative?

That's when absolute value really matters! If you get a negative number inside, the absolute value makes it positive. For example, $|3 - 8| = |-5| = 5$ .

How do I know when to use absolute value?

Look for the vertical bars $| |$ around an expression. These bars mean "find the distance from zero" - always a positive result!

Can the answer ever be negative?

Never! Absolute value always gives a non-negative result. If you get a negative answer, check your work - you likely made an error in the order of operations.

What's the difference between this and regular parentheses?

Both require you to work inside first, but absolute value bars have an extra step: after completing internal operations, you must make the result non-negative (positive or zero).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Absolute Value and Inequality questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime