Evaluate -(-1)^100 × 2²: Step-by-Step Solution Guide

Negative Exponents with Order of Operations

−(−1)100⋅22= -(-1)^{100}\cdot2^2=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 First, let's calculate the sign
00:07 Even power, therefore the sign will be positive
00:14 Let's calculate the square
00:20 1 to any power is always equal to 1
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

−(−1)100⋅22= -(-1)^{100}\cdot2^2=

2

Step-by-step solution

To solve this problem, we need to evaluate −(−1)100⋅22-(-1)^{100}\cdot2^2.

  • Step 1: Calculate (−1)100(-1)^{100}. Since 100 is an even number, (−1)100=1(-1)^{100} = 1.
  • Step 2: Calculate 222^2. This gives us 44.
  • Step 3: Multiply the results from the first two steps: 1⋅4=41 \cdot 4 = 4.
  • Step 4: Apply the negative sign: −4-4.

Thus, when evaluating the expression, we find that the correct result is −4-4.

3

Final Answer

−4 -4

Key Points to Remember

Essential concepts to master this topic
  • Exponent Rule: Even powers of negative numbers are always positive
  • Technique: Calculate (−1)100=1 (-1)^{100} = 1 then multiply by 4
  • Check: Final result includes the outer negative sign: −(1⋅4)=−4 -(1 \cdot 4) = -4 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the outer negative sign
    Don't calculate just (−1)100⋅22=1⋅4=4 (-1)^{100} \cdot 2^2 = 1 \cdot 4 = 4 ! This ignores the negative sign at the front and gives a positive result instead of negative. Always apply the outer negative sign last: −((−1)100⋅22)=−4 -((-1)^{100} \cdot 2^2) = -4 .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why is (−1)100 (-1)^{100} equal to 1?

+

When you raise -1 to an even power, the result is always positive 1! This is because you multiply -1 by itself an even number of times, and negative × negative = positive.

What's the difference between (−1)100 (-1)^{100} and −(1)100 -(1)^{100} ?

+

(−1)100 (-1)^{100} means the entire negative number is raised to the 100th power, giving 1. But −(1)100 -(1)^{100} means you raise 1 to the 100th power first, then apply the negative sign, giving -1.

How do I handle the outer negative sign?

+

Think of it as two separate steps: first calculate everything inside the parentheses, then apply the negative sign at the very end. So −((−1)100⋅22)=−(1⋅4)=−4 -((-1)^{100} \cdot 2^2) = -(1 \cdot 4) = -4 .

What if the exponent was odd, like 101?

+

Then (−1)101=−1 (-1)^{101} = -1 because odd powers of negative numbers stay negative. Your final answer would be −(−1⋅4)=−(−4)=4 -(-1 \cdot 4) = -(-4) = 4 .

Why do we follow order of operations here?

+

Order of operations (PEMDAS) tells us to handle exponents before multiplication, and the negative sign outside acts like multiplication by -1, which comes last.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers - special cases questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Powers of Negative Numbers

Solve (-(-2)²)² - 2³: Multiple Exponents and Negative Numbers
Click to solve
Evaluate (-5)³ + 5²: Combining Cube and Square Powers
Click to solve