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March 10th, 2016, 02:33 AM  #1 
Newbie Joined: Mar 2016 From: India Posts: 14 Thanks: 0  Fractional Exponents
Hi Experts Can you please help me to find Fractional exponents value For Eg: 2^1/3 Thank You in advance 
March 10th, 2016, 02:36 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
$\displaystyle 2^{1/3} = \sqrt[3]{2} \approx 1.26$

March 10th, 2016, 02:40 AM  #3 
Newbie Joined: Mar 2016 From: India Posts: 14 Thanks: 0  
March 10th, 2016, 02:47 AM  #4  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,801 Thanks: 636 Math Focus: Yet to find out.  Quote:
But if you really feel like fiddling around, then (for this case) you need to find a number that can be cubed (multiplied by itself 3 times) which will equal 2. EDIT: Remember to not post your questions in the New Users section! Welcome to MMF Please do not post math questions here Last edited by Joppy; March 10th, 2016 at 02:51 AM.  
March 10th, 2016, 03:18 AM  #5 
Newbie Joined: Mar 2016 From: India Posts: 14 Thanks: 0 
okay sir and Is there any possibility to solve with logarithms ?

March 10th, 2016, 03:23 AM  #6  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
1) Let f(x) = 2^(1/3)  x. f(x) is continuous and differentiable everywhere on R, and you know that, say, f(0) > 0 and f(2) < 0. By the intermediate value theorem, you know the root is on (0, 2), so you apply the bisection method or Newton's method. 2) Let f(x) = 2^x. Find an appropriate Taylor approximation, i.e. f(a) + f'(a)(xa) + f''(a)(xa)^2/2! + f'''(a)(xa)^3/3! + ... for x=1/3 and a = 0.  
March 10th, 2016, 03:25 AM  #7  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
And actually, my Taylor approximation suggestion has lots of ln 2s in it, so I guess it uses logarithms Last edited by 123qwerty; March 10th, 2016 at 03:27 AM.  
March 10th, 2016, 06:18 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,417 Thanks: 1025 
8^(1/3) = 2 : digging a hole where all is soft earth... 2^(1/3) = ~1.26 : digging hole where earth is crusty, and lots of stones 

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exponents, fractional 
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