Evaluate -(-1)^80: Double Negative with Exponent Problem

Exponent Rules with Order of Operations

−(−1)80= -(-1)^{80}=

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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
00:08 Even power, therefore the sign will be positive
00:22 Let's calculate the power, 1 to any power is always equal to 1
00:27 Negative times positive is always negative
00:31 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)80= -(-1)^{80}=

2

Step-by-step solution

To solve this problem, we'll evaluate the expression −(−1)80-(-1)^{80}.

  • Step 1: Evaluate (−1)80(-1)^{80}.

Since the exponent 80 is an even number, by applying the rule for negative powers, (−1)80=1(-1)^{80} = 1.

  • Step 2: Apply the negation.

The expression is −(−1)80-(-1)^{80}, which simplifies to −1-1, because negating 1 results in −1-1.

Therefore, the solution to the problem is −1-1.

3

Final Answer

−1 -1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Even exponents make negative bases positive: (−1)80=1 (-1)^{80} = 1
  • Technique: Apply order of operations: exponent first, then negative sign outside
  • Check: Verify: −1×1=−1 -1 \times 1 = -1 ✓

Common Mistakes

Avoid these frequent errors
  • Applying the negative sign before the exponent
    Don't calculate (−(−1))80 (-(-1))^{80} first = 180=1 1^{80} = 1 ! This ignores order of operations and gives the wrong answer. Always evaluate the exponent first, then apply the negative sign outside.

Practice Quiz

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\( (-2)^7= \)

FAQ

Everything you need to know about this question

Why doesn't the negative sign affect the exponent calculation?

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The negative sign is outside the parentheses, so by order of operations, we calculate (−1)80 (-1)^{80} first, then apply the negative. Think of it as −1×((−1)80) -1 \times ((-1)^{80}) .

How do I remember that even exponents make negative numbers positive?

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Even exponents = positive result because you multiply an even number of negative signs together. For example: (−1)×(−1)=+1 (-1) \times (-1) = +1 , and this pattern continues for all even powers!

What would happen if the exponent was 81 instead of 80?

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With an odd exponent like 81, (−1)81=−1 (-1)^{81} = -1 , so the final answer would be −(−1)=+1 -(-1) = +1 instead. Odd exponents keep the negative sign!

Is this different from (−(−1)80) (-(-1)^{80}) ?

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No! These expressions are exactly the same. The parentheses around the negative don't change anything - both follow the same order of operations: exponent first, then the negative sign.

Why can't I just cancel the two negative signs?

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You can't "cancel" them because they're applied at different steps! One negative is the base (-1), the other is outside the entire expression. Follow order of operations step by step instead.

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