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March 10th, 2016, 02:33 AM   #1
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Fractional Exponents

Hi Experts

Can you please help me to find Fractional exponents value

For Eg: 2^1/3
Thank You in advance
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March 10th, 2016, 02:36 AM   #2
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$\displaystyle 2^{1/3} = \sqrt[3]{2} \approx 1.26$
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March 10th, 2016, 02:40 AM   #3
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Quote:
Originally Posted by 123qwerty View Post
$\displaystyle 2^{1/3} = \sqrt[3]{2} \approx 1.26$
Value is okay sir but how you got it.what is procedural approach to solve such kind of problems
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March 10th, 2016, 02:47 AM   #4
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Quote:
Originally Posted by Prudhvi raj k View Post
Value is okay sir but how you got it.what is procedural approach to solve such kind of problems
You use a calculator.

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.
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March 10th, 2016, 03:18 AM   #5
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okay sir and Is there any possibility to solve with logarithms ?
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March 10th, 2016, 03:23 AM   #6
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Quote:
Originally Posted by Prudhvi raj k View Post
Value is okay sir but how you got it.what is procedural approach to solve such kind of problems
There are many ways you could use I guess...

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)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ... for x=1/3 and a = 0.
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March 10th, 2016, 03:25 AM   #7
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Quote:
Originally Posted by Prudhvi raj k View Post
okay sir and Is there any possibility to solve with logarithms ?
Doesn't that just make things even more complicated?

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.
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March 10th, 2016, 06:18 AM   #8
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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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