March 15th, 2017, 10:47 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, 10:53 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,322 Thanks: 452 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, 10:54 PM  #3 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 
$(1)^n = \begin{cases}\phantom{} 1&\text{n even}\\ 1 &\text{n odd}\end{cases}$

March 15th, 2017, 11:46 PM  #4 
Newbie Joined: Mar 2017 From: Australia Posts: 19 Thanks: 1 Math Focus: Algebra, Trigonometry, Calculus 
Oh, thank you!

March 15th, 2017, 11:54 PM  #5 
Member Joined: Sep 2016 From: India Posts: 88 Thanks: 30 
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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