Solve (-(2)²)²: Double Square with Negative Number

Order of Operations with Nested Exponents

((2)2)2= (-(2)^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 exponent without the sign, then place the sign afterwards
00:12 Break down the exponent into multiplications, and solve
00:16 Negative times negative always equals positive
00:21 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

((2)2)2= (-(2)^2)^2=

2

Step-by-step solution

To solve this problem, we'll methodically approach it by following these steps:

  • Step 1: Simplify the expression inside the parentheses.
  • Step 2: Evaluate the power applied to the result from Step 1.

Now, let's execute each step in detail:

Step 1: Simplify the expression inside the parentheses ((2)2) (-(2)^2) .

Calculate (2)2 (2)^2 :

22=4 2^2 = 4

Substitute back into the expression:

(2)2=4 -(2)^2 = -4

Step 2: Evaluate the expression (4)2 (-4)^2 .

Calculate the square:

(4)2=16 (-4)^2 = 16

The solution to the problem is 16 16 , which corresponds to choice 2.

3

Final Answer

16 16

Key Points to Remember

Essential concepts to master this topic
  • Rule: Evaluate exponents from innermost parentheses outward step by step
  • Technique: First calculate 22=4 2^2 = 4 , then (4)=4 -(4) = -4 , finally (4)2=16 (-4)^2 = 16
  • Check: Any negative number squared becomes positive: (4)2=(4)×(4)=16 (-4)^2 = (-4) \times (-4) = 16

Common Mistakes

Avoid these frequent errors
  • Ignoring the negative sign inside parentheses
    Don't calculate (22)2=42=16 (2^2)^2 = 4^2 = 16 and ignore the negative! This misses the crucial step where (2)2=4 -(2)^2 = -4 . Always work from inside the parentheses outward, applying the negative sign to get (4)2=16 (-4)^2 = 16 .

Practice Quiz

Test your knowledge with interactive questions

\( \)\( -(2)^2= \)

FAQ

Everything you need to know about this question

Why doesn't the negative sign make the final answer negative?

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Because we're squaring a negative number! When you multiply (4)×(4) (-4) \times (-4) , negative times negative equals positive. The negative sign is inside the parentheses that get squared.

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

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(2)2=(4)=4 -(2)^2 = -(4) = -4 because the negative applies after squaring. But (2)2=4 (-2)^2 = 4 because the negative is part of what gets squared.

How do I keep track of all the parentheses and exponents?

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Work step-by-step from the innermost operations outward. Write each step clearly: ((2)2)2(4)216 (-(2)^2)^2 \rightarrow (-4)^2 \rightarrow 16 . Don't try to do multiple steps at once!

What if I got -16 as my answer?

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You likely forgot that squaring always gives a positive result! Remember: (4)2=(4)×(4)=+16 (-4)^2 = (-4) \times (-4) = +16 . The exponent 2 applies to the entire (4) (-4) .

Can I use a calculator for problems like this?

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Yes, but be very careful with parentheses! Enter it exactly as (-(2^2))^2 to get the right answer. Missing parentheses will give you the wrong result.

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