# Solve? 8x^4=x

$x = \frac{1}{2}$

#### Explanation:

We have

$8 {x}^{4} = x$

We can first divide through by $x$:

$8 {x}^{3} = 1$

Let's now divide through by 8:

${x}^{3} = \frac{1}{8}$

Let's now take a second to see what we have. First remember that $8 = {2}^{3}$ and so $\frac{1}{8} = \frac{1}{2} ^ 3$. Let's substitute that in:

${x}^{3} = \frac{1}{2} ^ 3$

We can now take the cube root:

$\sqrt[3]{{x}^{3}} = \sqrt[3]{\frac{1}{2} ^ 3}$

$x = \frac{1}{2}$