Solve the Basic Equation: Finding Expressions Equal to 9

Q: What's the difference between $ (-3)^2 $ and $ -(3)^2 $ ?

The parentheses make all the difference! $ (-3)^2 $ means square the negative three = 9. But $ -(3)^2 $ means take the negative of three squared = -9.

Q: How do I remember which expressions equal 9?

Look for the negative number inside parentheses being squared. Only $ (-3)^2 $ has the negative completely enclosed before squaring, giving you a positive result.

Q: Why is $ -(-3)^2 $ equal to -9?

Work from inside out: first $ (-3)^2 = 9 $, then apply the outer negative sign: $ -(9) = -9 $. The double negative doesn't cancel here because of order of operations!

Q: Can a negative number ever equal 9?

No! The number 9 is positive, so no negative number or negative expression can equal 9. That's why $ -3 $ is immediately ruled out as an answer.

Exponent Rules with Negative Numbers

$9=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Break down to power

00:05 Let's break down the power to multiplication, excluding the sign

00:08 It seems this option is not suitable

00:12 Let's break down the power to multiplication, including the sign

00:16 This option is suitable

00:21 Let's break down the power to multiplication, excluding the sign

00:24 It seems this option is not suitable

00:27 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

$9=$

Step-by-step solution

To solve this problem, we need to evaluate expressions by applying the rules of exponents and the effects of parentheses on negative numbers:

$(-3)^2$ : When a negative number is squared, the result is positive. So, $(-3)^2$ means $-3 \times -3 = 9$ .
$-(-3)^2$ : This means $-1 \times (-3 \times -3)$ because squaring a number negates the negative sign inside parentheses, resulting in $-9$ .
$-(3)^2$ : This equals $-1 \times (3 \times 3) = -9$ , as the negative sign is outside the squared value.
$-3$ : This is simply $-3$ .

Only $(-3)^2$ equals 9, confirming it as the correct expression required by the problem.

Therefore, the solution to the problem is $(-3)^2$ .

Final Answer

$(-3)^2$

Key Points to Remember

Essential concepts to master this topic

Parentheses Rule: Negative numbers in parentheses change sign when squared
Technique: $(-3)^2 = (-3) \times (-3) = 9$
Check: Only $(-3)^2$ gives positive 9, others give -9 or -3 ✓

Common Mistakes

Avoid these frequent errors

Confusing placement of negative signs and parentheses
Don't treat $-(3)^2$ and $(-3)^2$ as the same = one gives -9, the other gives 9! The parentheses placement completely changes the result. Always square the negative number first when it's inside parentheses.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

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

FAQ

Everything you need to know about this question

Why does squaring a negative number make it positive?

When you multiply two negative numbers, you get a positive result! So $(-3)^2 = (-3) \times (-3) = +9$ . Think of it as negative times negative equals positive.

What's the difference between $(-3)^2$ and $-(3)^2$ ?

The parentheses make all the difference! $(-3)^2$ means square the negative three = 9. But $-(3)^2$ means take the negative of three squared = -9.

How do I remember which expressions equal 9?

Look for the negative number inside parentheses being squared. Only $(-3)^2$ has the negative completely enclosed before squaring, giving you a positive result.

Why is $-(-3)^2$ equal to -9?

Work from inside out: first $(-3)^2 = 9$ , then apply the outer negative sign: $-(9) = -9$ . The double negative doesn't cancel here because of order of operations!

Can a negative number ever equal 9?

No! The number 9 is positive, so no negative number or negative expression can equal 9. That's why $-3$ is immediately ruled out as an answer.

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Solve the Basic Equation: Finding Expressions Equal to 9

Exponent Rules with Negative Numbers

❤️ 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 does squaring a negative number make it positive?

What's the difference between $(-3)^2$ and $-(3)^2$ ?

How do I remember which expressions equal 9?

Why is $-(-3)^2$ equal to -9?

Can a negative number ever equal 9?

🌟 Unlock Your Math Potential

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Solve the Basic Equation: Finding Expressions Equal to 9

Exponent Rules with Negative Numbers

❤️ 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 does squaring a negative number make it positive?

What's the difference between (−3)2 (-3)^2 (−3)2 and −(3)2 -(3)^2 −(3)2?

How do I remember which expressions equal 9?

Why is −(−3)2 -(-3)^2 −(−3)2 equal to -9?

Can a negative number ever equal 9?

🌟 Unlock Your Math Potential

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What's the difference between $(-3)^2$ and $-(3)^2$ ?

Why is $-(-3)^2$ equal to -9?