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

1. ### Paencake

3
Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?

2. ### micromass

19,346
Staff Emeritus
It doesn't. It simplifies to

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

(assuming x is a real number)

3. ### Paencake

3
I don't understand why the exponents are disregarded.

4. ### Number Nine

782
They're not. Take the fourth root of each side.

5. ### symbolipoint

3,251
$\frac{1}{x^4}=(\frac{1}{x})^4$
$\sqrt{(\frac{1}{x})^4}=\pm(\frac{1}{x})^2$

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

Last edited by a moderator: Jan 2, 2013
6. ### symbolipoint

3,251
That's what I am trying to show but typesetting is not working.

3
Thanks.

12,317
Fixed.

9. ### symbolipoint

3,251
Thanks. Now by comparison of the tex code I can see my parenthesis mistake in one of them.

10. ### Char. Limit

1,986
Are we assuming x is real here? Because there's two other possibilities for x that yield the same answer.

11. ### coolul007

234
$x^{-4} = 4^{4}$

12. ### dextercioby

12,317
And even better:

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