Complete the Equation: Solving for the Value Equal to 8

Negative Exponents with Order of Operations

8= 8=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Break down to power
00:03 Let's break down the power into multiplication, including the sign
00:12 We see that the sign remains negative, so it doesn't fit
00:20 This option is exactly like the previous one, just multiplied by minus
00:26 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

8= 8=

2

Step-by-step solution

To solve this problem, let's evaluate both given expressions to determine which results in 8.

  • Step 1: Evaluate (−2)3(-2)^3:
    (−2)3=(−2)×(−2)×(−2)(-2)^3 = (-2) \times (-2) \times (-2).
    Multiplying across: (−2)×(−2)=4(-2) \times (-2) = 4, and then 4×(−2)=−84 \times (-2) = -8.
    Thus, (−2)3=−8(-2)^3 = -8.
  • Step 2: Evaluate −(−2)3-(-2)^3:
    First, calculate (−2)3(-2)^3 again: We already know (−2)3=−8(-2)^3 = -8.
    Now, apply the negative sign: −(−8)=8-(-8) = 8.

Therefore, the expression that equals 88 is −(−2)3-(-2)^3.

Thus, the correct expression that evaluates to 8 is −(−2)3-(-2)^3.

3

Final Answer

−(−2)3 -(-2)^3

Key Points to Remember

Essential concepts to master this topic
  • Exponent Rule: Negative base raised to odd power stays negative
  • Technique: Calculate (−2)3=−8 (-2)^3 = -8 , then apply outer negative: −(−8)=8 -(-8) = 8
  • Check: Verify by substituting: −(−2)3=−(−8)=8 -(-2)^3 = -(−8) = 8 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the placement of negative signs
    Don't calculate (−2)3 (-2)^3 as positive 8! When a negative number is raised to an odd power, the result is negative: (−2)3=−8 (-2)^3 = -8 . Always follow order of operations: exponent first, then apply any outside negative sign.

Practice Quiz

Test your knowledge with interactive questions

\( (-2)^7= \)

FAQ

Everything you need to know about this question

Why does (−2)3 (-2)^3 equal -8 and not 8?

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When you raise a negative number to an odd power, the result stays negative! (−2)3=(−2)×(−2)×(−2)=4×(−2)=−8 (-2)^3 = (-2) \times (-2) \times (-2) = 4 \times (-2) = -8 . Remember: negative × negative = positive, but positive × negative = negative.

What's the difference between (−2)3 (-2)^3 and −(−2)3 -(-2)^3 ?

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The placement of parentheses matters! (−2)3 (-2)^3 means 'negative 2 cubed' = -8. But −(−2)3 -(-2)^3 means 'the opposite of negative 2 cubed' = opposite of -8 = +8.

How do I remember the order of operations with negatives?

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PEMDAS still applies! Do what's in parentheses first, then exponents, then any negative signs outside. Think of the outer negative as 'multiply by -1' and do it last.

Why can't I just ignore the negative signs?

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Negative signs completely change your answer! In this problem, ignoring them would give you -8 instead of 8. Always track negative signs carefully - they're not optional!

What if the exponent was even instead of odd?

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With even exponents, negative bases become positive! For example: (−2)2=4 (-2)^2 = 4 . But with odd exponents like 3, the negative stays: (−2)3=−8 (-2)^3 = -8 .

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