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November 3rd, 2017, 11:23 AM   #1
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Solve. Answer only the positive solution.

Unless this is too hard to explain for me here I just need steps for where to go from when I get the 2.56E-6

in order to get it to a fraction. Thanks for any reply even if I can't have a shown process.
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November 3rd, 2017, 12:17 PM   #2
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Quote:
Originally Posted by GIjoefan1976 View Post
Unless this is too hard to explain for me here I just need steps for where to go from when I get the 2.56E-6

in order to get it to a fraction. Thanks for any reply even if I can't have a shown process.
$13 + 0.0005x^{-4} = 208.3125 \implies 0.0005x^{-4} = 195.3125 \implies \dfrac{0.005}{x^4} = 195.3125 \implies $

$x^4 = \dfrac{0.0005}{195.3125} = \dfrac{5 * 10^{-4}}{1.953125 * 10^2} = 2.56 * 10^{-6}.$

I take it that this is what you did. Well done. (It really does help to show what you have done so we we do not have to do work that is already done.)

Your problem here is that minus 6 is not divisible by 4. You need a simple trick: you multiply by 1.

$x^4 = 2.56 * 10^{-6} = 2.56 * 10^2 * 10^{-2} * 10^{-6} = 256 * 10^{-8} \implies.$

$x = \sqrt[4]{256 * 10^{-8}} = \sqrt[4]{256} * \sqrt[4]{10^{-8}} = 4 * 10^{-2} = \dfrac{4}{100} = \dfrac{1}{25}.$
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November 3rd, 2017, 01:13 PM   #3
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Quote:
Originally Posted by JeffM1 View Post
$13 + 0.0005x^{-4} = 208.3125 \implies 0.0005x^{-4} = 195.3125 \implies \dfrac{0.005}{x^4} = 195.3125 \implies $

$x^4 = \dfrac{0.0005}{195.3125} = \dfrac{5 * 10^{-4}}{1.953125 * 10^2} = 2.56 * 10^{-6}.$

I take it that this is what you did. Well done. (It really does help to show what you have done so we we do not have to do work that is already done.)

Your problem here is that minus 6 is not divisible by 4. You need a simple trick: you multiply by 1.

$x^4 = 2.56 * 10^{-6} = 2.56 * 10^2 * 10^{-2} * 10^{-6} = 256 * 10^{-8} \implies.$

$x = \sqrt[4]{256 * 10^{-8}} = \sqrt[4]{256} * \sqrt[4]{10^{-8}} = 4 * 10^{-2} = \dfrac{4}{100} = \dfrac{1}{25}.$
hello Jeffm1! Okay thanks very much...okay I will make sure to share the previous work from now on. I am still lost for where the 10^{6} came from? Is that just coming from the fact that we have two decimal places after the . so we have to use 100?
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November 3rd, 2017, 10:05 PM   #4
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Let's start by cleaning up my first post.

$13 + 0.0005x^{-4} = 208.3125$

$\implies 0.0005x^{-4} = 195.3125$

$\implies \dfrac{5 * 10^{-4}}{x^4} = 1.953125 * 10^2$

$\implies x^4 = \dfrac{5 * 10^{-4}}{1.953125 * 10^2} = 2.56 * 10^{(-\ 4 - 2)} = 2.56 * 10^{-6}.$

Is this what you did? If so, great. Now your second post asked where 10^6 came from? It does not come from anywhere because it is no where in the working. Are you ok up to here?

The problem in proceeding is that minus 6 is not divisible by 4. You need a simple trick: you multiply by

$1 = 10^0 = 10^{(2-2)} = 10^2 * 10^{-2}.$

Why 2 - 2? Because $-\ 6 - 2 = -\ 8 = 4(-\ 2).$

$x^4 = 2.56 * 10^{-6} = 2.56 * 10^2 * 10^{-2} * 10^{-6} = 2.56 * 100 * 10^{-8} = 256 * 10^{-8}.$

Any questions up to here? If so, where exactly?

$\therefore x = \sqrt[4]{256 * 10^{-8}} = \sqrt[4]{256} * \sqrt[4]{10^{-8}} = 4 * 10^{-2} = \dfrac{4}{100} = \dfrac{1}{25}.$

Sorry for the bad formatting in the first post. Now that it is easier to read, do you still have questions?
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