Evaluate the Absolute Value in Exponentiation: Solve |(-4)^2|

Q: Why don't we make -4 positive before squaring?

Because the order of operations tells us to do exponents before absolute value! The parentheses around -4 mean we square the entire negative number first: $(-4)^2$.

Q: What's the difference between (-4)² and -4²?

$(-4)^2 = 16$ because we square the negative number. But $-4^2 = -16$ because we take the negative of 4 squared. Parentheses matter!

Q: Will the absolute value always be the same as the original?

Not always! If $(-3)^3 = -27$, then $|(-3)^3| = |-27| = 27$. It depends on whether the result inside is positive or negative.

Q: Why is (-4)² positive but (-4)³ would be negative?

Even exponents always give positive results when applied to negative numbers, but odd exponents keep the negative sign. $(-4)^2 = 16$ but $(-4)^3 = -64$.

Exponentiation with Absolute Value Operations

$|(-4)^2| =$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$|(-4)^2| =$

Step-by-step solution

First, calculate $(-4)^2$ .

The expression $(-4)^2$ means $-4 \times -4$ .

Calculating this gives $16$ .

The absolute value of $16$ is still $16$ , since the absolute value of a positive number is itself.

Final Answer

$16$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate the exponent first, then apply absolute value
Technique: $(-4)^2 = (-4) \times (-4) = 16$
Check: Since 16 is positive, $|16| = 16$ ✓

Common Mistakes

Avoid these frequent errors

Applying absolute value before exponentiation
Don't calculate $|{-4}|^2 = 4^2 = 16$ first! While this gives the same answer here, it creates confusion with order of operations. Always follow the correct sequence: exponentiation happens before absolute value operations.

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 make -4 positive before squaring?

Because the order of operations tells us to do exponents before absolute value! The parentheses around -4 mean we square the entire negative number first: $(-4)^2$ .

What's the difference between (-4)² and -4²?

$(-4)^2 = 16$ because we square the negative number. But $-4^2 = -16$ because we take the negative of 4 squared. Parentheses matter!

Will the absolute value always be the same as the original?

Not always! If $(-3)^3 = -27$ , then $|(-3)^3| = |-27| = 27$ . It depends on whether the result inside is positive or negative.

How do I remember when to use absolute value bars?

The absolute value bars are part of the original expression - they're given to you! Just follow order of operations: parentheses, exponents, then absolute value.

Why is (-4)² positive but (-4)³ would be negative?

Even exponents always give positive results when applied to negative numbers, but odd exponents keep the negative sign. $(-4)^2 = 16$ but $(-4)^3 = -64$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Absolute Value and Inequality questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime