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1/(x^4) = 4^4 simplifies to 1/x = 4

by Paencake
Tags: 1 or x, 1 or x4, simplifies
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Paencake
#1
Dec29-12, 04:39 PM
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Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?
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micromass
#2
Dec29-12, 04:41 PM
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It doesn't. It simplifies to

[tex]1/x=4~\text{or}~1/x=-4[/tex]

(assuming x is a real number)
Paencake
#3
Dec29-12, 04:51 PM
P: 3
I don't understand why the exponents are disregarded.

Number Nine
#4
Dec29-12, 05:03 PM
P: 772
1/(x^4) = 4^4 simplifies to 1/x = 4

Quote Quote by Paencake View Post
I don't understand why the exponents are disregarded.
They're not. Take the fourth root of each side.
symbolipoint
#5
Dec29-12, 05:05 PM
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[itex]\frac{1}{x^4}=(\frac{1}{x})^4[/itex]
[itex]\sqrt{(\frac{1}{x})^4}=\pm(\frac{1}{x})^2 [/itex]

[itex]\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x} [/itex]
symbolipoint
#6
Dec29-12, 05:08 PM
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Quote Quote by Number Nine View Post
They're not. Take the fourth root of each side.
That's what I am trying to show but typesetting is not working.
Paencake
#7
Dec29-12, 05:08 PM
P: 3
Quote Quote by Number Nine View Post
They're not. Take the fourth root of each side.
Thanks.
dextercioby
#8
Dec29-12, 05:26 PM
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Quote Quote by symbolipoint View Post
[itex]\frac{1}{x^4}=(\frac{1}{x})^4[/itex]
[itex]\sqrt{(\frac{1}{x})^4}=\pm (\frac{1}{x})^2 [/itex]

[itex]\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x} [/itex]
Fixed.
symbolipoint
#9
Dec29-12, 11:24 PM
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Quote Quote by dextercioby View Post
Fixed.
Thanks. Now by comparison of the tex code I can see my parenthesis mistake in one of them.
Char. Limit
#10
Dec30-12, 08:41 AM
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Are we assuming x is real here? Because there's two other possibilities for x that yield the same answer.
coolul007
#11
Dec30-12, 02:50 PM
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[itex]x^{-4} = 4^{4}[/itex]
dextercioby
#12
Dec30-12, 02:54 PM
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And even better:

[tex] x^{-4} = \left(\frac{1}{4}\right)^{-4} [/tex]


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