Calculate the Absolute Value of the Power: Solving |(-3)^2|

Q: Why is (-3)² positive when -3 is negative?

When you square a negative number, you get a positive result because negative × negative = positive. So $ (-3)^2 = (-3) \times (-3) = 9 $.

Q: Does the absolute value change anything here?

Not in this case! Since $ (-3)^2 = 9 $ is already positive, the absolute value $ |9| = 9 $ doesn't change the result.

Q: What if the exponent was 3 instead of 2?

Then you'd get $ (-3)^3 = -27 $ (negative), so $ |(-3)^3| = |-27| = 27 $. Even exponents give positive results, odd exponents keep the original sign.

Q: How do I remember the order of operations here?

Use PEMDAS! Parentheses first (nothing here), then Exponents $ (-3)^2 $, then other operations like absolute value come after.

Q: Is |(-3)²| the same as |-3|²?

No! The first is $ |(-3)^2| = |9| = 9 $. The second is $ |-3|^2 = 3^2 = 9 $. They happen to give the same answer, but that's just coincidence for this example.

Absolute Value with Negative Base Powers

$|(-3)^2| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|(-3)^2| =$

Step-by-step solution

First, calculate $(-3)^2$ , which equals $9$ . The absolute value of $9$ is simply $9$ because it is positive.

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Calculate the power before applying absolute value
Technique: Evaluate $(-3)^2 = 9$ first, then find absolute value
Check: Since 9 is already positive, $|9| = 9$ ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value before calculating the power
Don't compute $|(-3)|^2 = 3^2 = 9$ instead of the given expression! This changes the problem completely and gives the same answer by coincidence. Always follow order of operations: calculate $(-3)^2$ first, then apply absolute value.

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 (-3)² positive when -3 is negative?

When you square a negative number, you get a positive result because negative × negative = positive. So $(-3)^2 = (-3) \times (-3) = 9$ .

Does the absolute value change anything here?

Not in this case! Since $(-3)^2 = 9$ is already positive, the absolute value $|9| = 9$ doesn't change the result.

What if the exponent was 3 instead of 2?

Then you'd get $(-3)^3 = -27$ (negative), so $|(-3)^3| = |-27| = 27$ . Even exponents give positive results, odd exponents keep the original sign.

How do I remember the order of operations here?

Use PEMDAS! Parentheses first (nothing here), then Exponents $(-3)^2$ , then other operations like absolute value come after.

Is |(-3)²| the same as |-3|²?

No! The first is $|(-3)^2| = |9| = 9$ . The second is $|-3|^2 = 3^2 = 9$ . They happen to give the same answer, but that's just coincidence for this example.

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