Question
\( \left. \begin{array} { l } { - 8 ^ { 6 } = \square } \\ { ( - 8 ) ^ { 6 } = \square } \end{array} \right. \)
Ask by Donnelly Guerrero. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
–8⁶ = –262144
(–8)⁶ = 262144
Solution
Let's evaluate each expression step by step.
1. For –8⁶:
According to the order of operations, exponentiation comes before the application of the negative sign. Thus, –8⁶ is interpreted as –(8⁶). Since 8⁶ = 262144, we have:
–8⁶ = –262144.
2. For (–8)⁶:
Here the negative sign is inside the parentheses, so it is the entire –8 that is raised to the 6th power. Since 6 is an even exponent, the result will be positive. Calculating (–8)⁶ gives:
(–8)⁶ = 262144.
So, the answers are:
–8⁶ = –262144
(–8)⁶ = 262144.
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Simplify this solution Mind Expander
When you compute \( -8^6 \), you're actually squaring -8 to the sixth power without the parentheses around -8, which gives you \( -1 \times 8^6 \). So, you end up with a negative number, \( -262144 \). On the other hand, \( (-8)^6 \) involves raising -8 to the sixth power, which gives \( 8^6 = 262144 \). Here, the negative sign goes away because you're multiplying an even number of negative factors. Always watch those parentheses!
