Evaluate the Absolute Value of the Power: What is |4²|?

Q: Why don't we take the absolute value of 4 first?

Order of operations! Exponents come before absolute value. We must calculate $ 4^2 = 16 $ first, then find $ |16| = 16 $.

Q: What if the base was negative, like (-4)²?

Great question! $ (-4)^2 = 16 $ (positive), so $ |(-4)^2| = |16| = 16 $. The result is the same because squaring always gives a positive result.

Q: Does the absolute value sign change anything here?

Not in this case! Since $ 4^2 = 16 $ is already positive, the absolute value doesn't change it. But it's still important to follow the correct order.

Q: How is this different from |4|²?

$ |4|^2 $ means find the absolute value first: $ |4| = 4 $, then square: $ 4^2 = 16 $. Same answer here, but different process!

Q: Will the answer always be positive?

Yes! Absolute value always gives a non-negative result. Since we're taking the absolute value of $ 4^2 $, the final answer must be positive or zero.

Absolute Value with Perfect Squares

$|4^2| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|4^2| =$

Step-by-step solution

To solve the expression $|4^2|$ , first calculate $4^2$ , which equals $16$ . The absolute value of $16$ is $16$ since it is already positive.

Final Answer

$16$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate the exponent first, then apply absolute value
Technique: $4^2 = 16$ , then $|16| = 16$
Check: Since $4^2$ gives positive 16, absolute value stays 16 ✓

Common Mistakes

Avoid these frequent errors

Applying absolute value before calculating the exponent
Don't find |4| first then square it = still gets 16, but wrong method! This confuses the order of operations and can lead to errors with negative bases. Always calculate exponents first, then apply absolute value 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 don't we take the absolute value of 4 first?

Order of operations! Exponents come before absolute value. We must calculate $4^2 = 16$ first, then find $|16| = 16$ .

What if the base was negative, like (-4)²?

Great question! $(-4)^2 = 16$ (positive), so $|(-4)^2| = |16| = 16$ . The result is the same because squaring always gives a positive result.

Does the absolute value sign change anything here?

Not in this case! Since $4^2 = 16$ is already positive, the absolute value doesn't change it. But it's still important to follow the correct order.

How is this different from |4|²?

$|4|^2$ means find the absolute value first: $|4| = 4$ , then square: $4^2 = 16$ . Same answer here, but different process!

Will the answer always be positive?

Yes! Absolute value always gives a non-negative result. Since we're taking the absolute value of $4^2$ , the final answer must be positive or zero.

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