Evaluate the Expression: |6² - 10| Step by Step

Q: Why do I calculate the exponent first instead of the absolute value?

The order of operations (PEMDAS) applies inside absolute value bars too! You must complete all operations inside the bars before applying the absolute value to the result.

Q: Can I break this into separate absolute values?

No! $ |6^2 - 10| $ is NOT the same as $ |6^2| - |10| $. You must do all operations inside the bars first, then apply absolute value once.

Q: How do I remember the order of operations with absolute value?

Think of absolute value bars like parentheses - you must finish everything inside them first! So treat $ |6^2 - 10| $ like $ (6^2 - 10) $, then make the final answer positive.

Absolute Value with Exponent Operations

$|6^2 - 10| =$

❤️ 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

$|6^2 - 10| =$

Step-by-step solution

First, calculate $6^2$ . That is, $6 \times 6 = 36$ .

Next, subtract 10 from 36: $36 - 10 = 26$ .

Finally, the absolute value of 26 is $|26| = 26$ since it is already a positive number.

Final Answer

$26$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Always evaluate exponents before subtraction inside absolute value
Technique: Calculate 6² = 36, then 36 - 10 = 26
Check: Since 26 is positive, |26| = 26 stays the same ✓

Common Mistakes

Avoid these frequent errors

Applying absolute value before completing operations inside
Don't calculate |6²| - |10| = 36 - 10 = 26! This changes the order of operations and can give wrong answers when the inside expression is negative. Always complete all operations inside the absolute value bars first, then apply absolute value to the final 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 do I calculate the exponent first instead of the absolute value?

The order of operations (PEMDAS) applies inside absolute value bars too! You must complete all operations inside the bars before applying the absolute value to the result.

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

If we had gotten a negative number like -5, then the absolute value would make it positive: $|-5| = 5$ . Absolute value always gives a non-negative result.

Can I break this into separate absolute values?

No! $|6^2 - 10|$ is NOT the same as $|6^2| - |10|$ . You must do all operations inside the bars first, then apply absolute value once.

How do I remember the order of operations with absolute value?

Think of absolute value bars like parentheses - you must finish everything inside them first! So treat $|6^2 - 10|$ like $(6^2 - 10)$ , then make the final answer positive.

What's the difference between 26 and |26|?

When a number is already positive (like 26), the absolute value doesn't change it: $|26| = 26$ . Absolute value only changes negative numbers to positive.

🌟 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