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November 3rd, 2017, 11:23 AM  #1 
Senior Member Joined: Feb 2016 From: seattle Posts: 370 Thanks: 10  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 2.56E6 in order to get it to a fraction. Thanks for any reply even if I can't have a shown process. 
November 3rd, 2017, 12:17 PM  #2  
Senior Member Joined: May 2016 From: USA Posts: 825 Thanks: 335  Quote:
$x^4 = \dfrac{0.0005}{195.3125} = \dfrac{5 * 10^{4}}{1.953125 * 10^2} = 2.56 * 10^{6}.$ 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. $x^4 = 2.56 * 10^{6} = 2.56 * 10^2 * 10^{2} * 10^{6} = 256 * 10^{8} \implies.$ $x = \sqrt[4]{256 * 10^{8}} = \sqrt[4]{256} * \sqrt[4]{10^{8}} = 4 * 10^{2} = \dfrac{4}{100} = \dfrac{1}{25}.$  
November 3rd, 2017, 01:13 PM  #3  
Senior Member Joined: Feb 2016 From: seattle Posts: 370 Thanks: 10  Quote:
 
November 3rd, 2017, 10:05 PM  #4 
Senior Member Joined: May 2016 From: USA Posts: 825 Thanks: 335 
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 $1 = 10^0 = 10^{(22)} = 10^2 * 10^{2}.$ 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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