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

1. Dec 29, 2012

Paencake

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

2. Dec 29, 2012

micromass

Staff Emeritus
It doesn't. It simplifies to

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

(assuming x is a real number)

3. Dec 29, 2012

Paencake

I don't understand why the exponents are disregarded.

4. Dec 29, 2012

Number Nine

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

5. Dec 29, 2012

symbolipoint

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

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

Last edited by a moderator: Jan 2, 2013
6. Dec 29, 2012

symbolipoint

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

7. Dec 29, 2012

Paencake

Thanks.

8. Dec 29, 2012

dextercioby

Fixed.

9. Dec 29, 2012

symbolipoint

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

10. Dec 30, 2012

Char. Limit

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

11. Dec 30, 2012

coolul007

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

12. Dec 30, 2012

dextercioby

And even better:

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