Compare Expressions: -2(3)² vs -(−6)² | Order of Operations Challenge

Q: Why is (-6)² positive but -(-6)² negative?

The parentheses make the difference! $ (-6)^2 $ means square the negative six, giving 36. But $ -(-6)^2 $ means take the negative of (-6)², so you get -36.

Q: How do I remember which negative number is larger?

Think of a number line! Numbers to the right are always larger. Since -18 is to the right of -36, we have -18 > -36. Remember: less negative means larger!

Q: Does -2·(3)² equal (-2·3)²?

No! Order of operations matters. $ -2 \cdot (3)^2 = -2 \cdot 9 = -18 $, but $ (-2 \cdot 3)^2 = (-6)^2 = 36 $. Always do exponents before multiplication!

Q: Why do we need parentheses around the 3 in (3)²?

The parentheses in $ (3)^2 $ don't change the calculation - they're just for clarity. Whether you write $ 3^2 $ or $ (3)^2 $, both equal 9.

Q: What's the difference between -6² and (-6)²?

$ -6^2 = -(6^2) = -36 $ (negative of six squared)$ (-6)^2 = 36 $ (negative six, all squared)The parentheses completely change the meaning!

Order of Operations with Negative Exponents

Which is larger?

$-2\cdot(3)^2⬜-(-6)^2$

❤️ 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 Place the appropriate sign

00:03 Let's calculate the exponent and continue solving

00:07 Now let's calculate the sign of the second exponent

00:12 Even exponent, therefore the sign will be positive

00:15 Let's calculate the exponent

00:23 Negative times positive is always negative

00:27 Let's compare the numbers

00:30 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

Which is larger?

$-2\cdot(3)^2⬜-(-6)^2$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate the expression $-2 \cdot (3)^2$ .
Step 2: Evaluate the expression $-(-6)^2$ .
Step 3: Compare the results of Step 1 and Step 2.

Now, let's work through each step:

Step 1: Calculate $-2 \cdot (3)^2$ .

First, find $(3)^2$ . Since $3^2 = 9$ , we have:

$-2 \cdot (3)^2 = -2 \cdot 9 = -18$ .

Step 2: Calculate $-(-6)^2$ .

First, find $(-6)^2$ . Calculating the square gives:

$(-6)^2 = 36$ .

Apply the negative sign: $-(-6)^2 = -36$ .

Step 3: Compare the results.

We have $-2 \cdot (3)^2 = -18$ and $-(-6)^2 = -36$ .

Since $-18$ is larger than $-36$ , we conclude:

The expression $-2 \cdot (3)^2$ is greater than $-(-6)^2$ .

Therefore, the solution to the problem is $>$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: Exponents come before multiplication in order of operations
Technique: Calculate (-6)² = 36, then apply negative: -(-6)² = -36
Check: Compare -18 and -36 on number line: -18 > -36 ✓

Common Mistakes

Avoid these frequent errors

Applying the negative sign before squaring
Don't calculate -(-6)² as (-(-6))² = 6² = 36! This ignores order of operations and gives a positive result instead of negative. Always square first, then apply the outer negative sign: (-6)² = 36, so -(-6)² = -36.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

$$ $$ (-8)^2= $$

FAQ

Everything you need to know about this question

Why is (-6)² positive but -(-6)² negative?

The parentheses make the difference! $(-6)^2$ means square the negative six, giving 36. But $-(-6)^2$ means take the negative of (-6)², so you get -36.

How do I remember which negative number is larger?

Think of a number line! Numbers to the right are always larger. Since -18 is to the right of -36, we have -18 > -36. Remember: less negative means larger!

Does -2·(3)² equal (-2·3)²?

No! Order of operations matters. $-2 \cdot (3)^2 = -2 \cdot 9 = -18$ , but $(-2 \cdot 3)^2 = (-6)^2 = 36$ . Always do exponents before multiplication!

Why do we need parentheses around the 3 in (3)²?

The parentheses in $(3)^2$ don't change the calculation - they're just for clarity. Whether you write $3^2$ or $(3)^2$ , both equal 9.

What's the difference between -6² and (-6)²?

$-6^2 = -(6^2) = -36$ (negative of six squared)
$(-6)^2 = 36$ (negative six, all squared)

The parentheses completely change the meaning!

🌟 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