Find All Expressions Equal to 36: Complete Number Decomposition

Q: Why does (-6)² equal positive 36?

When you multiply two negative numbers, you get a positive result! So $ (-6) \times (-6) = +36 $. The parentheses make sure the negative sign is part of what gets squared.

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

Parentheses matter! In $ (-6)^2 $, the negative is squared too. In $ -(6)^2 $, only 6 gets squared, then we apply the negative: $ -(36) = -36 $.

Q: How do I remember when negatives become positive?

Use the rule: negative × negative = positive. When squaring a negative number in parentheses like $ (-6)^2 $, you're multiplying the negative by itself!

Q: Are there other expressions that equal 36?

Yes! Try $ 6^2 $, $ \sqrt{1296} $, or $ 4 \times 9 $. But remember, only expressions with the correct order of operations will work.

Q: What if I wrote 6² instead of (-6)²?

That gives you $ 6^2 = 36 $ too, but it's a different expression! Both $ 6^2 $ and $ (-6)^2 $ equal 36, showing that both positive and negative numbers can have the same square.

Exponent Operations with Negative Numbers

$36=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Start by breaking down the exponent step by step.

00:07 Now, let's express the exponent as a multiplication problem. Remember to include the sign.

00:12 Great job! Let's keep going. This looks like a good approach.

00:17 Next, break the exponent into multiplication again, but this time, exclude the sign.

00:22 And there you have it! That's how we find the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$36=$

Step-by-step solution

To determine which expression equals 36, we need to consider how squaring works with negative numbers:
Step 1: Consider the expression $(-6)^2$ . This means that we take -6 and multiply it by itself:
$(-6) \times (-6) = 36$

Step 2: Consider the expression $-(6)^2$ . Here, the square acts only on 6, not on the negative sign in front because of the absence of parentheses around -6:
$-(6 \times 6) = -36$

Therefore, the expression $(-6)^2$ correctly equals 36.

The correct choice that satisfies $36 =$ is $(-6)^2$ .

Final Answer

$(-6)^2$

Key Points to Remember

Essential concepts to master this topic

Parentheses Rule: $(-6)^2$ means multiply negative by itself
Order of Operations: $(-6) \times (-6) = 36$ because negatives make positive
Check: Substitute back: $(-6)^2 = 36$ ✓

Common Mistakes

Avoid these frequent errors

Confusing parentheses placement with negative signs
Don't think $-(6)^2$ equals 36 = wrong answer -36! The negative sign outside parentheses applies after squaring. Always check if parentheses include the negative sign: $(-6)^2 = 36$ but $-(6)^2 = -36$ .

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

Why does (-6)² equal positive 36?

When you multiply two negative numbers, you get a positive result! So $(-6) \times (-6) = +36$ . The parentheses make sure the negative sign is part of what gets squared.

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

Parentheses matter! In $(-6)^2$ , the negative is squared too. In $-(6)^2$ , only 6 gets squared, then we apply the negative: $-(36) = -36$ .

How do I remember when negatives become positive?

Use the rule: negative × negative = positive. When squaring a negative number in parentheses like $(-6)^2$ , you're multiplying the negative by itself!

Are there other expressions that equal 36?

Yes! Try $6^2$ , $\sqrt{1296}$ , or $4 \times 9$ . But remember, only expressions with the correct order of operations will work.

What if I wrote 6² instead of (-6)²?

That gives you $6^2 = 36$ too, but it's a different expression! Both $6^2$ and $(-6)^2$ equal 36, showing that both positive and negative numbers can have the same square.

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