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March 15th, 2017, 10:47 PM   #1
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Exponents

Why is (-5)^3 = -125 but (-10)^4 = 10,000
With one you end up with a negative and the other a positive.
Something special about cubed?
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March 15th, 2017, 10:53 PM   #2
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Write them out long hand (repeated multiplication). Then make up some of your own examples to further verify the recurring pattern.

You should find that even powers (in your case, 4) will always yield a positive result. Whereas odd powers (in your case, 3) will yield a negative result IF the base is negative.

Experiment!
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March 15th, 2017, 10:54 PM   #3
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$(-1)^n = \begin{cases}\phantom{-} 1&\text{n even}\\ -1 &\text{n odd}\end{cases}$
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March 15th, 2017, 11:46 PM   #4
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Oh, thank you!
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March 15th, 2017, 11:54 PM   #5
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Since, $Negative\times Negative=Positive$

and

$Postive\times Negative=Negative$

Therefore,

$\begin{equation} \begin{split}(-5)^3 &=(-5)\times(-5)\times(-5)\\ &=25\times(-5)\\ &=-125\\(-10)^4 &=(-10)\times(-10)\times(-10)\times(-10)\\ &=(100)\times(100)\\ &=10000\end{split}\end{equation}$
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