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

$$ (-2)^7= $$

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?