Solve -(-6)²: Order of Operations with Negative Squares

Q: Why doesn't the negative sign cancel out when we square?

The negative sign outside the parentheses isn't part of what gets squared! Only $(-6)$ gets squared to equal 36, then we apply the outer negative sign to get $-36$.

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

In $-(-6)^2$, only $(-6)$ gets squared first. In $(-(-6))^2$, we simplify inside parentheses first to get $6^2 = 36$. Parentheses placement matters!

Q: How do I remember the order of operations here?

Use PEMDAS! First handle what's in parentheses $(-6)^2$, then apply the negative sign outside. Think of it as two separate steps.

Q: Will the answer always be negative in problems like this?

Not always! It depends on the expression. $-(-6)^2 = -36$ is negative, but $-(-6)^3 = -(-216) = 216$ would be positive because we're negating a negative result.

Q: What if there was no parentheses around -6?

Without parentheses, $--6^2$ would mean $-(6^2) = -36$. The result is the same here, but parentheses make the order crystal clear and prevent confusion!

Negative Signs with Squared Parentheses

$-(-6)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 First let's calculate the sign

00:07 Even power, therefore the sign will be positive

00:11 Now let's calculate the power

00:26 Negative times positive always equals negative

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

$-(-6)^2=$

Step-by-step solution

To solve the problem of evaluating $-(-6)^2$ , we will follow these steps:

Step 1: Calculate the square of $-6$ .
Step 2: Apply the negative sign to the result obtained from the first step.

Let's work through these steps:
Step 1: Calculate $(-6)^2$ . We know that when squaring a negative number, the result becomes positive: $(-6) \times (-6) = 36$ .
Step 2: Now apply the negative sign to this result. The expression is $-(36)$ , which equals $-36$ .

Therefore, the solution to the problem is $-36$ .

Final Answer

$-36$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Parentheses first, then exponents, then multiplication/division
Technique: Calculate $(-6)^2 = 36$ , then apply the negative sign
Check: Verify $-(-6)^2 = -(36) = -36$ follows PEMDAS correctly ✓

Common Mistakes

Avoid these frequent errors

Applying the negative sign before squaring
Don't calculate $(-(-6))^2 = 6^2 = 36$ ! This ignores order of operations and treats the outer negative as part of the base. Always square first: $(-6)^2 = 36$ , then apply the negative: $-(36) = -36$ .

Practice Quiz

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

FAQ

Everything you need to know about this question

Why doesn't the negative sign cancel out when we square?

The negative sign outside the parentheses isn't part of what gets squared! Only $(-6)$ gets squared to equal 36, then we apply the outer negative sign to get $-36$ .

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

In $-(-6)^2$ , only $(-6)$ gets squared first. In $(-(-6))^2$ , we simplify inside parentheses first to get $6^2 = 36$ . Parentheses placement matters!

How do I remember the order of operations here?

Use PEMDAS! First handle what's in parentheses $(-6)^2$ , then apply the negative sign outside. Think of it as two separate steps.

Will the answer always be negative in problems like this?

Not always! It depends on the expression. $-(-6)^2 = -36$ is negative, but $-(-6)^3 = -(-216) = 216$ would be positive because we're negating a negative result.

What if there was no parentheses around -6?

Without parentheses, $--6^2$ would mean $-(6^2) = -36$ . The result is the same here, but parentheses make the order crystal clear and prevent confusion!

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Solve -(-6)²: Order of Operations with Negative Squares

Negative Signs with Squared Parentheses

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why doesn't the negative sign cancel out when we square?

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

How do I remember the order of operations here?

Will the answer always be negative in problems like this?

What if there was no parentheses around -6?

🌟 Unlock Your Math Potential

More Questions

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Evaluate -(-2)³: Working with Negative Numbers and Exponents

Solve (-(2)²)²: Double Square with Negative Number

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Solve the Exponent Problem: Finding (-8)² Using Order of Operations

Solve -(-6)²: Order of Operations with Negative Squares

Negative Signs with Squared Parentheses

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why doesn't the negative sign cancel out when we square?

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

How do I remember the order of operations here?

Will the answer always be negative in problems like this?

What if there was no parentheses around -6?

🌟 Unlock Your Math Potential

More Questions

Powers of Negative Numbers

Evaluate -(-2)³: Working with Negative Numbers and Exponents

Solve (-(2)²)²: Double Square with Negative Number

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

Solve the Exponent Problem: Finding (-8)² Using Order of Operations

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