Solve |(9-3)²|: Absolute Value of a Squared Difference

Q: Why is the absolute value of 36 still 36?

The absolute value of any positive number is just itself! Since $ 6^2 = 36 $ is already positive, $ |36| = 36 $.

Q: Do I always square first, then take absolute value?

Follow the order of operations! Work from the inside out: parentheses first, then exponents, then absolute value. So $ |(9-3)^2| $ becomes $ |6^2| $, then $ |36| $.

Q: What's the difference between |6²| and |6|²?

Great question! $ |6^2| = |36| = 36 $, but $ |6|^2 = 6^2 = 36 $. They're the same here because 6 is positive, but with negative numbers, the order matters!

Order of Operations with Absolute Values

$\left|(9 - 3)^2\right| =$

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Step-by-step written solution

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Understand the problem

$\left|(9 - 3)^2\right| =$

Step-by-step solution

The expression $\left|(9 - 3)^2\right|$ represents the absolute value of the square of $(9 - 3)$ .

Calculate the difference: $9 - 3 = 6$ .

Then compute the square: $6^2 = 36$ .

The absolute value of $36$ is $36$ .

Final Answer

$36$

Key Points to Remember

Essential concepts to master this topic

Rule: Operations inside absolute value bars are calculated first
Technique: Work from inside out: (9-3) = 6, then 6² = 36
Check: Since 36 is positive, |36| = 36 stays the same ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value before completing all operations
Don't calculate |9-3|² = |6|² = 6² = 36! This changes the order and can give wrong results with negative numbers. Always complete everything inside the absolute value bars first, then apply the 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 is the absolute value of 36 still 36?

The absolute value of any positive number is just itself! Since $6^2 = 36$ is already positive, $|36| = 36$ .

What if the result inside was negative?

Then the absolute value would make it positive! For example, if we had $|(-4)^2|$ , we'd get $|16| = 16$ , which is still positive.

Do I always square first, then take absolute value?

Follow the order of operations! Work from the inside out: parentheses first, then exponents, then absolute value. So $|(9-3)^2|$ becomes $|6^2|$ , then $|36|$ .

Could any of the wrong answers be right?

No way! 9 would mean we forgot to square, -6 is impossible since absolute values are never negative, and saying "no absolute value" ignores the bars completely.

What's the difference between |6²| and |6|²?

Great question! $|6^2| = |36| = 36$ , but $|6|^2 = 6^2 = 36$ . They're the same here because 6 is positive, but with negative numbers, the order matters!

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