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

Q: Why is the answer negative when we're squaring something?

The outer negative sign is applied after the squaring! We square $ (-9)^2 = 81 $ first, then apply the final negative to get $ -81 $.

Q: How do I keep track of all these negative signs?

Work step by step and write each result clearly. Start from the innermost parentheses and move outward, keeping track of each negative sign as you go.

Q: Does the order really matter that much?

Absolutely! Changing the order gives completely different answers. $ -(-(3)^2)^2 = -81 $ but $ (-(-(3)^2))^2 = 81 $ - see the difference?

Q: What if I get confused by the double negatives?

Replace each step with its value as you go. After $ (3)^2 = 9 $, rewrite as $ -(-(9))^2 $, then $ -(-9)^2 $, and finally $ -81 $.

Q: How can I double-check my work?

Use the substitution method: replace the original expression step by step with calculated values. Each intermediate result should make sense with PEMDAS rules.

Order of Operations with Nested Negatives

$-(-(3)^2)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Calculate the power without the sign, then apply the sign afterwards

00:12 Break down the power into multiplications, and solve

00:24 Negative times negative always equals positive

00:32 Negative times positive always equals negative

00:37 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

$-(-(3)^2)^2=$

Step-by-step solution

To solve the expression $-(-(3)^2)^2$ , we will strictly follow the order of operations, PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Step 1: Evaluate the inner exponent.
We compute $(3)^2 = 9$ .
Step 2: Apply the first negative sign.
The expression becomes $-((3)^2) = -(9) = -9$ .
Step 3: Apply the second negative sign and exponent.
Now, simplify $-(-9)^2$ .
First, evaluate the exponent: $(-9)^2 = (-9) \times (-9) = 81$ .
Then, apply the negative sign: $-81$ .

Therefore, the solution to the problem is $-81$ .

Final Answer

$-81$

Key Points to Remember

Essential concepts to master this topic

Rule: Evaluate innermost operations first, then work outward systematically
Technique: $(3)^2 = 9$ , then $-(9) = -9$ , then $(-9)^2 = 81$
Check: Final negative makes $-81$ ; verify each step matches PEMDAS ✓

Common Mistakes

Avoid these frequent errors

Applying negative signs before completing exponents
Don't calculate $-3^2 = -9$ and then square to get 81! This ignores proper order and gives a positive result instead of -81. Always complete all operations inside parentheses first, then apply outer negatives.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

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

FAQ

Everything you need to know about this question

Why is the answer negative when we're squaring something?

The outer negative sign is applied after the squaring! We square $(-9)^2 = 81$ first, then apply the final negative to get $-81$ .

How do I keep track of all these negative signs?

Work step by step and write each result clearly. Start from the innermost parentheses and move outward, keeping track of each negative sign as you go.

Does the order really matter that much?

Absolutely! Changing the order gives completely different answers. $-(-(3)^2)^2 = -81$ but $(-(-(3)^2))^2 = 81$ - see the difference?

What if I get confused by the double negatives?

Replace each step with its value as you go. After $(3)^2 = 9$ , rewrite as $-(-(9))^2$ , then $-(-9)^2$ , and finally $-81$ .

How can I double-check my work?

Use the substitution method: replace the original expression step by step with calculated values. Each intermediate result should make sense with PEMDAS rules.

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