Solve -(7²): Understanding the Order of Operations with Negative Squares

Q: What's the difference between -(7)² and (-7)²?

Big difference! In $ -(7)^2 $, you square 7 first (getting 49), then apply the negative (getting -49). In $ (-7)^2 $, you square the entire negative number, so negative times negative equals positive, giving you +49.

Q: Why isn't the answer just 49?

The negative sign is outside the parentheses! This means it's not part of what gets squared. Think of it as $ -1 \times (7)^2 $ - you multiply the result of 7² by -1.

Q: Does the negative sign get squared too?

No! The negative sign is not inside the parentheses, so it doesn't get affected by the exponent. Only the 7 gets squared, then we apply the negative to that result.

Q: How can I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Here, exponents come before the multiplication by -1, so $ 7^2 $ happens first!

Q: What if there were no parentheses around the 7?

It would be the same! $ -7^2 $ also equals -49 because exponents have higher priority than the negative sign. The parentheses around 7 don't change the order of operations here.

Order of Operations with Negative Exponents

$-(7)^2=$

❤️ 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

00:00 Solve

00:03 Let's calculate the exponent, the sign is not part of the exponent

00:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-(7)^2=$

Step-by-step solution

The given problem asks us to evaluate the expression $-(7)^2$ . To solve this, we must correctly handle the operations of exponentiation and negation.

Firstly, examine $(7)^2$ :
- $(7)^2$ means multiplying 7 by itself.
- Calculating this gives: $7 \times 7 = 49$ .

Next, apply the negative sign to the result:
- The expression $-(7)^2$ indicates that we apply the negative sign to the result of $(7)^2$ .
- Therefore, multiply the result by $-1$ :
$-1 \times 49 = -49$ .

Thus, the correct evaluation of the expression is $-49$ .

Thus, the solution to this problem is $-49$ .

Final Answer

$-49$

Key Points to Remember

Essential concepts to master this topic

Rule: Apply exponent first, then apply the negative sign
Technique: Calculate $(7)^2 = 49$ , then apply negative: $-(49) = -49$
Check: Verify exponent gives positive 49, then negative makes it -49 ✓

Common Mistakes

Avoid these frequent errors

Applying the negative sign before the exponent
Don't calculate $(-7)^2 = 49$ instead of $-(7)^2 = -49$ ! The parentheses placement matters - without them around the negative, you square 7 first, then apply the minus sign. Always follow order of operations: exponents before multiplication (including by -1).

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

What's the difference between -(7)² and (-7)²?

Big difference! In $-(7)^2$ , you square 7 first (getting 49), then apply the negative (getting -49). In $(-7)^2$ , you square the entire negative number, so negative times negative equals positive, giving you +49.

Why isn't the answer just 49?

The negative sign is outside the parentheses! This means it's not part of what gets squared. Think of it as $-1 \times (7)^2$ - you multiply the result of 7² by -1.

Does the negative sign get squared too?

No! The negative sign is not inside the parentheses, so it doesn't get affected by the exponent. Only the 7 gets squared, then we apply the negative to that result.

How can I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Here, exponents come before the multiplication by -1, so $7^2$ happens first!

What if there were no parentheses around the 7?

It would be the same! $-7^2$ also equals -49 because exponents have higher priority than the negative sign. The parentheses around 7 don't change the order of operations here.

🌟 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