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 March 15th, 2017, 11:47 PM #1 Newbie   Joined: Mar 2017 From: Australia Posts: 19 Thanks: 1 Math Focus: Algebra, Trigonometry, Calculus 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?
 March 15th, 2017, 11:53 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,469 Thanks: 492 Math Focus: Yet to find out. 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!
 March 15th, 2017, 11:54 PM #3 Senior Member     Joined: Sep 2015 From: USA Posts: 1,692 Thanks: 860 $(-1)^n = \begin{cases}\phantom{-} 1&\text{n even}\\ -1 &\text{n odd}\end{cases}$
 March 16th, 2017, 12:46 AM #4 Newbie   Joined: Mar 2017 From: Australia Posts: 19 Thanks: 1 Math Focus: Algebra, Trigonometry, Calculus Oh, thank you!
 March 16th, 2017, 12:54 AM #5 Member   Joined: Sep 2016 From: India Posts: 88 Thanks: 30 Since, $Negative\times Negative=Positive$ and $Postive\times Negative=Negative$ Therefore, $$$\begin{split}(-5)^3 &=(-5)\times(-5)\times(-5)\\ &=25\times(-5)\\ &=-125\\(-10)^4 &=(-10)\times(-10)\times(-10)\times(-10)\\ &=(100)\times(100)\\ &=10000\end{split}$$$ Thanks from faaarwest2k

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