Evaluate -(2)²: Order of Operations with Negative Squares

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

Great question! $ -(2)^2 $ means "the negative of 2 squared" = -4, while $ (-2)^2 $ means "negative 2, squared" = +4. The position of parentheses completely changes the answer!

Q: Why does the negative sign come after squaring?

Because of the order of operations (PEMDAS)! Exponents come before multiplication/negation. Think of the negative sign as multiplying by -1, which happens after the exponent.

Q: How can I remember which operation comes first?

Use this trick: "What's attached to the base?" In $ -(2)^2 $, only the 2 is being squared. In $ (-2)^2 $, the entire -2 is being squared.

Q: What if the problem was $ -(-2)^2 $ ?

Then you'd get $ -(-2)^2 = -(+4) = -4 $. The $ (-2)^2 $ part gives +4 (negative times negative), then the outside negative makes it -4.

Negative Signs with Squared Expressions

$-(2)^2=$

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Step-by-step video solution

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00:00 Solve

00:03 Let's calculate the power without the sign, then we'll place the sign afterwards

00:07 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

$-(2)^2=$

Step-by-step solution

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

Step 1: Calculate $(2)^2$
Step 2: Apply the negative sign

Now, let's work through each step:
Step 1: Calculate $(2)^2$ . This is equal to $2 \times 2 = 4$ .
Step 2: Apply the negative sign: The expression $-(2)^2$ now becomes $-4$ .

Therefore, the value of the expression $-(2)^2$ is $-4$ .

This matches choice 4, which is $-4$ .

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Exponents come before applying the negative sign
Technique: Calculate $(2)^2 = 4$ first, then apply negative
Check: Verify by following PEMDAS: parentheses, exponents, then negation gives -4 ✓

Common Mistakes

Avoid these frequent errors

Applying the negative sign before squaring
Don't calculate $(-2)^2 = 4$ first! This gives +4 instead of -4 because you're squaring the negative. The expression $-(2)^2$ means "negative of 2 squared", not "negative 2, then squared". Always square first, then apply the negative sign outside.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

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

Great question! $-(2)^2$ means "the negative of 2 squared" = -4, while $(-2)^2$ means "negative 2, squared" = +4. The position of parentheses completely changes the answer!

Why does the negative sign come after squaring?

Because of the order of operations (PEMDAS)! Exponents come before multiplication/negation. Think of the negative sign as multiplying by -1, which happens after the exponent.

How can I remember which operation comes first?

Use this trick: "What's attached to the base?" In $-(2)^2$ , only the 2 is being squared. In $(-2)^2$ , the entire -2 is being squared.

Would $-2^2$ be the same as $-(2)^2$ ?

Yes! Both equal -4. When there are no parentheses around the base, like in $-2^2$ , we still square the 2 first, then apply the negative sign.

What if the problem was $-(-2)^2$ ?

Then you'd get $-(-2)^2 = -(+4) = -4$ . The $(-2)^2$ part gives +4 (negative times negative), then the outside negative makes it -4.

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Evaluate -(2)²: Order of Operations with Negative Squares

Negative Signs with Squared Expressions

❤️ 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

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

Why does the negative sign come after squaring?

How can I remember which operation comes first?

Would $-2^2$ be the same as $-(2)^2$ ?

What if the problem was $-(-2)^2$ ?

🌟 Unlock Your Math Potential

More Questions

Powers of Negative Numbers

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

Solve -(-(3)²)²: Double Negative with Square Numbers

Calculate (-1)^99: Evaluating Powers of Negative One

Solve: Evaluating -(-1)^100 with Double Negatives

Evaluate -(2)²: Order of Operations with Negative Squares

Negative Signs with Squared Expressions

❤️ 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

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

Why does the negative sign come after squaring?

How can I remember which operation comes first?

Would −22 -2^2 −22 be the same as −(2)2 -(2)^2 −(2)2?

What if the problem was −(−2)2 -(-2)^2 −(−2)2?

🌟 Unlock Your Math Potential

More Questions

Powers of Negative Numbers

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

Solve -(-(3)²)²: Double Negative with Square Numbers

Calculate (-1)^99: Evaluating Powers of Negative One

Solve: Evaluating -(-1)^100 with Double Negatives

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

Would $-2^2$ be the same as $-(2)^2$ ?

What if the problem was $-(-2)^2$ ?