Solve the Equation: Finding the Value Equal to -16

Q: Why does (-4)² equal positive 16 instead of negative 16?

When you have parentheses around a negative number, the entire negative number gets squared. So $(-4)^2 = (-4) \times (-4) = 16$. Remember: negative times negative equals positive!

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

Great question! $-4^2 = -(4^2) = -16$ because you square 4 first, then apply the negative. But $(-4)^2 = 16$ because the negative is inside the parentheses and gets squared too.

Q: How do I handle the negative sign in front of (-4)²?

Work from the inside out! First calculate $(-4)^2 = 16$, then apply the outer negative sign: $-(16) = -16$. The negative outside acts like multiplying by -1.

Q: Why can't both answers be correct if they use the same numbers?

The placement of parentheses and negative signs matters! $(-4)^2 = 16$ while $-(-4)^2 = -16$. Math is precise - even small changes in notation create different values.

Q: How can I remember the order of operations with negatives?

Use PEMDAS! Parentheses first, then Exponents, then Multiplication/Division. So in $-(-4)^2$: do parentheses $(-4)$, then exponent $^2$, then the outer negative (multiplication by -1).

Order of Operations with Negative Exponents

$-16=$

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's start by breaking down the exponent.

00:06 Separate the exponent into multiplication steps, but ignore the sign for now.

00:11 This method works great!

00:14 Now, include the sign as you continue to break it down.

00:18 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-16=$

Step-by-step solution

To solve this problem, we'll need to carefully consider the placement of parentheses and the order of operations when dealing with negative numbers and exponentiation:

Step 1: Examine the given expression $(-4)^2$ . This indicates squaring the entire negative four, which results in $16$ .
Step 2: Now, examine $-(-4)^2$ paying close attention to the negative sign in front. $(-4)^2$ again results in $16$ , but placing a minus before it changes its sign to $-16$ .

Let's analyze each possible choice:

For choice 1: The expression is $-(-4)^2$ . Calculating $(-4)^2$ gives $16$ , and applying the negative sign outside results in the expression value of $-16$ .
For choice 2: The expression is $(-4)^2$ , calculated to give $16$ .

Therefore, the expression that correctly equals $-16$ is choice 1, represented by $-(-4)^2$ .

The correct answer is choice 1: $-(-4)^2$ .

Final Answer

$-(-4)^2$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative signs outside parentheses apply after exponentiation
Technique: Calculate $(-4)^2 = 16$ , then apply outer negative: $-16$
Check: Verify $-(-4)^2 = -(16) = -16$ matches the target ✓

Common Mistakes

Avoid these frequent errors

Applying negative signs incorrectly with exponents
Don't think $(-4)^2 = -16$ ! Squaring a negative number always gives positive, so $(-4)^2 = 16$ . Always remember that parentheses around negative numbers get squared together, making the result positive.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

Why does (-4)² equal positive 16 instead of negative 16?

When you have parentheses around a negative number, the entire negative number gets squared. So $(-4)^2 = (-4) \times (-4) = 16$ . Remember: negative times negative equals positive!

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

Great question! $-4^2 = -(4^2) = -16$ because you square 4 first, then apply the negative. But $(-4)^2 = 16$ because the negative is inside the parentheses and gets squared too.

How do I handle the negative sign in front of (-4)²?

Work from the inside out! First calculate $(-4)^2 = 16$ , then apply the outer negative sign: $-(16) = -16$ . The negative outside acts like multiplying by -1.

Why can't both answers be correct if they use the same numbers?

The placement of parentheses and negative signs matters! $(-4)^2 = 16$ while $-(-4)^2 = -16$ . Math is precise - even small changes in notation create different values.

How can I remember the order of operations with negatives?

Use PEMDAS! Parentheses first, then Exponents, then Multiplication/Division. So in $-(-4)^2$ : do parentheses $(-4)$ , then exponent $^2$ , then the outer negative (multiplication by -1).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers - special cases 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