Evaluate -6²: Understanding Negative Numbers and Exponents

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

-6² means -(6²) = -36, while (-6)² means (-6) × (-6) = 36. The parentheses make a huge difference! Without parentheses, the negative sign stays outside the exponent.

Q: Why do we calculate the exponent before the negative?

Because of the order of operations (PEMDAS)! Exponents come before multiplication, and the negative sign is really multiplying by -1. So we do 6² first, then multiply by -1.

Q: How can I remember which way is correct?

Think of it as -1 × 6². You wouldn't change 6² to (-6)² when multiplying by -1, right? The negative sign is separate from the base number unless there are parentheses.

Q: What if the problem was written as -(6²)?

That would give the same answer: -36! Writing -(6²) makes it super clear that we square 6 first, then apply the negative sign. It's just a more obvious way to show the order of operations.

Q: Are there any tricks to avoid this mistake?

Yes! Always ask yourself: "What's being squared?" If only the number is being squared (like in -6²), then apply the negative after. If the negative is included (like in (-6)²), then square the whole thing including the negative.

Order of Operations with Negative Signs

$-6^2=$

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Step-by-step video solution

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00:00 Solve

00:04 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

$-6^2=$

Step-by-step solution

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

Step 1: Recognize the order of operations.
Step 2: Evaluate the exponent first before applying any operations outside the exponent.
Step 3: Apply the negative sign to the result of the squared value.

Now, let's work through each step:
Step 1: The expression $-6^2$ involves squaring the number 6. According to the order of operations, we compute exponents before multiplying by -1.
Step 2: This means we first calculate $6^2$ , which is equal to 36.
Step 3: After evaluating the square, apply the negative sign: $-6^2 = -(6^2) = -36$ .

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

Final Answer

$-36$

Key Points to Remember

Essential concepts to master this topic

Rule: Exponents are calculated before applying negative signs outside
Technique: Calculate $6^2 = 36$ first, then apply negative to get -36
Check: Verify that $-6^2 = -(6^2) = -36$ , not $(-6)^2 = 36$ ✓

Common Mistakes

Avoid these frequent errors

Treating -6² as (-6)²
Don't square the negative sign along with the number = 36 instead of -36! The negative sign is outside the exponent operation and gets applied after. Always calculate the exponent first, then apply the negative sign: -6² = -(6²) = -36.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

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

-6² means -(6²) = -36, while (-6)² means (-6) × (-6) = 36. The parentheses make a huge difference! Without parentheses, the negative sign stays outside the exponent.

Why do we calculate the exponent before the negative?

Because of the order of operations (PEMDAS)! Exponents come before multiplication, and the negative sign is really multiplying by -1. So we do 6² first, then multiply by -1.

How can I remember which way is correct?

Think of it as -1 × 6². You wouldn't change 6² to (-6)² when multiplying by -1, right? The negative sign is separate from the base number unless there are parentheses.

What if the problem was written as -(6²)?

That would give the same answer: -36! Writing -(6²) makes it super clear that we square 6 first, then apply the negative sign. It's just a more obvious way to show the order of operations.

Are there any tricks to avoid this mistake?

Yes! Always ask yourself: "What's being squared?" If only the number is being squared (like in -6²), then apply the negative after. If the negative is included (like in (-6)²), then square the whole thing including the negative.

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