Evaluate |3³ - 5|: Absolute Value of Powers Expression

Q: Why do I calculate the exponent before subtracting?

Follow the order of operations (PEMDAS)! Exponents come before subtraction. So $ 3^3 - 5 $ means calculate $ 3^3 = 27 $ first, then subtract 5.

Q: Do I need to show every step when calculating 3³?

Yes, especially when learning! Write $ 3^3 = 3 \times 3 \times 3 = 9 \times 3 = 27 $ to avoid calculation errors and show your understanding.

Q: Can absolute value bars change the order of operations?

No! Think of absolute value bars like parentheses. You must complete everything inside first using normal order of operations, then apply the absolute value at the very end.

Q: How do I know when my answer should be positive or negative?

Absolute value answers are always non-negative (positive or zero, never negative). If you get a negative final answer, you made an error somewhere!

Absolute Value with Exponent Calculations

$|3^3 - 5| =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|3^3 - 5| =$

Step-by-step solution

First, calculate $3^3$ . That is, $3 \times 3 \times 3 = 27$ .

Next, subtract 5 from 27: $27 - 5 = 22$ .

Finally, the absolute value of 22 is $|22| = 22$ since it is already a positive number.

Final Answer

$22$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate exponent first, then subtract, then absolute value
Technique: Compute $3^3 = 27$ , then $27 - 5 = 22$
Check: Since 22 is positive, $|22| = 22$ ✓

Common Mistakes

Avoid these frequent errors

Taking absolute value before completing calculations inside
Don't find $|3^3| - |5| = 27 - 5 = 22$ ! This happens to work but misses the point. Always complete everything inside the absolute value bars first: $3^3 - 5 = 22$ , then take $|22| = 22$ .

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 do I calculate the exponent before subtracting?

Follow the order of operations (PEMDAS)! Exponents come before subtraction. So $3^3 - 5$ means calculate $3^3 = 27$ first, then subtract 5.

What if the result inside the absolute value bars is negative?

The absolute value makes it positive! For example, if you had $|5 - 27| = |-22| = 22$ . The absolute value always gives a non-negative result.

Do I need to show every step when calculating 3³?

Yes, especially when learning! Write $3^3 = 3 \times 3 \times 3 = 9 \times 3 = 27$ to avoid calculation errors and show your understanding.

Can absolute value bars change the order of operations?

No! Think of absolute value bars like parentheses. You must complete everything inside first using normal order of operations, then apply the absolute value at the very end.

How do I know when my answer should be positive or negative?

Absolute value answers are always non-negative (positive or zero, never negative). If you get a negative final answer, you made an error somewhere!

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