Solve: Finding -|4²| Using Order of Operations

Q: Why isn't the answer positive 16?

The negative sign is outside the absolute value bars! So we first find $ |4^2| = |16| = 16 $, then apply the negative to get $ -16 $.

Q: Does the negative sign go inside the absolute value?

No! The expression is $ -|4^2| $, not $ |-4^2| $. The negative sign is outside the absolute value bars, so it gets applied after we calculate the absolute value.

Q: What if I computed |4²| first and got confused?

That's the right first step! $ |4^2| = |16| = 16 $. The key is remembering that the negative sign outside means you take the opposite of the absolute value result.

Q: Can absolute values ever be negative?

Absolute values themselves are never negative - they're always zero or positive. But when you have a negative sign outside the absolute value (like $ -|x| $), the final result can be negative.

Order of Operations with Negative Absolute Values

$-\lvert4^2\rvert=$

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Understand the problem

$-\lvert4^2\rvert=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Compute the expression inside the absolute value.
Step 2: Apply the absolute value.
Step 3: Apply the negative sign.

Now, let's work through each step:
Step 1: Compute $4^2$ .
Since $4^2 = 16$ , we have $\lvert 4^2 \rvert = \lvert 16 \rvert$ .
Step 2: Apply the absolute value operation. The absolute value of 16 is 16, so $\lvert 16 \rvert = 16$ .
Step 3: Apply the negative sign. We then have $-\lvert 16 \rvert = -16$ .

Therefore, the solution to the problem is $-16$ .

Final Answer

$-16$

Key Points to Remember

Essential concepts to master this topic

Order: First compute inside absolute value, then apply absolute value
Technique: Calculate $4^2 = 16$ , then $|16| = 16$ , finally apply negative
Check: Work step-by-step: $-|4^2| = -|16| = -16$ ✓

Common Mistakes

Avoid these frequent errors

Applying the negative sign before the absolute value
Don't compute $|-4^2| = |-16| = 16$ ! This changes the order of operations and gives a positive result instead of negative. Always follow order of operations: compute inside absolute value first, then apply absolute value, then apply the negative sign outside.

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 isn't the answer positive 16?

The negative sign is outside the absolute value bars! So we first find $|4^2| = |16| = 16$ , then apply the negative to get $-16$ .

Does the negative sign go inside the absolute value?

No! The expression is $-|4^2|$ , not $|-4^2|$ . The negative sign is outside the absolute value bars, so it gets applied after we calculate the absolute value.

What if I computed |4²| first and got confused?

That's the right first step! $|4^2| = |16| = 16$ . The key is remembering that the negative sign outside means you take the opposite of the absolute value result.

Can absolute values ever be negative?

Absolute values themselves are never negative - they're always zero or positive. But when you have a negative sign outside the absolute value (like $-|x|$ ), the final result can be negative.

How do I remember the order of operations here?

Think of it like parentheses: the absolute value bars act like grouping symbols. So you work inside first ( $4^2 = 16$ ), then apply the absolute value ( $|16| = 16$ ), then any operations outside (the negative sign).

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