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

$$1/x=4~\text{or}~1/x=-4$$

(assuming x is a real number)

 

[Paencake]

I don't understand why the exponents are disregarded.

 

[Number Nine]

I don't understand why the exponents are disregarded.

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

 

[symbolipoint]

$\frac{1}{x^4}=(\frac{1}{x})^4$
$\sqrt{(\frac{1}{x})^4}=\pm(\frac{1}{x})^2$

$\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x}$

 

[symbolipoint]

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

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

 

[Paencake]

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

Thanks.

 

[dextercioby]

$\frac{1}{x^4}=(\frac{1}{x})^4$
$\sqrt{(\frac{1}{x})^4}=\pm (\frac{1}{x})^2$

$\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x}$

Fixed.

 

[symbolipoint]

Fixed.

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]

$x^{-4} = 4^{4}$

 

[dextercioby]

And even better:

$$x^{-4} = \left(\frac{1}{4}\right)^{-4}$$ :tongue2: