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

Paencake

Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?

micromass

It doesn't. It simplifies to

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

(assuming x is a real number)

Paencake

I don't understand why the exponents are disregarded.

Number Nine

They're not. Take the fourth root of each side.

symbolipoint

[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

That's what I am trying to show but typesetting is not working.

Paencake

Thanks.

dextercioby

Fixed.

symbolipoint

Thanks. Now by comparison of the tex code I can see my parenthesis mistake in one of them.

Char. Limit

Are we assuming x is real here? Because there's two other possibilities for x that yield the same answer.

coolul007

[itex]x^{-4} = 4^{4}[/itex]

dextercioby

And even better:

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