Solve for Absolute Value in the Expression |6^2|

Q: Why don't we get both +36 and -36 as answers?

Absolute value always gives you one non-negative result. The expression $ |6^2| $ means "the absolute value of 36," which is simply 36. You're not solving an equation like $ x^2 = 36 $.

Q: What if the base was negative, like (-6)²?

Great question! $ |(-6)^2| = |36| = 36 $ because squaring a negative number gives a positive result. The absolute value of any positive number is just itself.

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

Always follow order of operations (PEMDAS)! Exponents come before absolute value, so calculate $ 6^2 = 36 $ first, then find $ |36| = 36 $.

Q: Can absolute value ever make a number negative?

Never! Absolute value measures distance from zero, which is always non-negative. $ |\text{any number}| \geq 0 $ always.

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

They're the same in this case: $ |6^2| = |36| = 36 $ and $ |6|^2 = 6^2 = 36 $. But with negative numbers, $ |(-3)^2| = 9 $ while $ |-3|^2 = 9 $ - they happen to equal each other!

Absolute Value with Perfect Squares

$\left|6^2\right|=$

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Step-by-step written solution

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Understand the problem

$\left|6^2\right|=$

Step-by-step solution

The expression given is the absolute value of the square of 6, written as $\left|6^2\right|$ . First, calculate the square of 6: $6^2 = 36$ . Since the absolute value of a number is its non-negative value, the absolute value of 36 is simply 36. Thus, $\left|6^2\right| = 36$ , which means the correct answer is $36$ .

Final Answer

$36$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Calculate the exponent first, then find absolute value
Technique: Evaluate $6^2 = 36$ , then $|36| = 36$
Check: Since 36 is positive, its absolute value remains 36 ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value before calculating the exponent
Don't find |6| = 6 first, then square to get 36! This happens to give the right answer here but fails with negative bases. Always follow order of operations: calculate 6² = 36 first, then find |36| = 36.

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 don't we get both +36 and -36 as answers?

Absolute value always gives you one non-negative result. The expression $|6^2|$ means "the absolute value of 36," which is simply 36. You're not solving an equation like $x^2 = 36$ .

What if the base was negative, like (-6)²?

Great question! $|(-6)^2| = |36| = 36$ because squaring a negative number gives a positive result. The absolute value of any positive number is just itself.

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

Always follow order of operations (PEMDAS)! Exponents come before absolute value, so calculate $6^2 = 36$ first, then find $|36| = 36$ .

Can absolute value ever make a number negative?

Never! Absolute value measures distance from zero, which is always non-negative. $|\text{any number}| \geq 0$ always.

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

They're the same in this case: $|6^2| = |36| = 36$ and $|6|^2 = 6^2 = 36$ . But with negative numbers, $|(-3)^2| = 9$ while $|-3|^2 = 9$ - they happen to equal each other!

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