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

by Paencake
Tags: 1 or x, 1 or x4, simplifies
 P: 3 Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?
 Mentor P: 18,225 It doesn't. It simplifies to $$1/x=4~\text{or}~1/x=-4$$ (assuming x is a real number)
 P: 3 I don't understand why the exponents are disregarded.
P: 772
1/(x^4) = 4^4 simplifies to 1/x = 4

 Quote by Paencake I don't understand why the exponents are disregarded.
They're not. Take the fourth root of each side.
 HW Helper PF Gold P: 2,813 $\frac{1}{x^4}=(\frac{1}{x})^4$ $\sqrt{(\frac{1}{x})^4}=\pm(\frac{1}{x})^2$ $\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x}$
HW Helper
PF Gold
P: 2,813
 Quote by Number Nine They're not. Take the fourth root of each side.
That's what I am trying to show but typesetting is not working.
P: 3
 Quote by Number Nine They're not. Take the fourth root of each side.
Thanks.
HW Helper
P: 11,915
 Quote by symbolipoint $\frac{1}{x^4}=(\frac{1}{x})^4$ $\sqrt{(\frac{1}{x})^4}=\pm (\frac{1}{x})^2$ $\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x}$
Fixed.
HW Helper
PF Gold
P: 2,813
 Quote by dextercioby Fixed.
Thanks. Now by comparison of the tex code I can see my parenthesis mistake in one of them.
 PF Gold P: 1,951 Are we assuming x is real here? Because there's two other possibilities for x that yield the same answer.
 P: 234 $x^{-4} = 4^{4}$
 Sci Advisor HW Helper P: 11,915 And even better: $$x^{-4} = \left(\frac{1}{4}\right)^{-4}$$

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