Solve for h 256=4h^6

$256 = 4 h^{6}$

Step 1

Rewrite the equation as $4 h^{6} = 256$ .

$4 h^{6} = 256$

Step 2

Divide each term in $4 h^{6} = 256$ by $4$ and simplify.

Divide each term in $4 h^{6} = 256$ by $4$ .

$\frac{4 h^{6}}{4} = \frac{256}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 h^{6}}{4} = \frac{256}{4}$

Divide $h^{6}$ by $1$ .

$h^{6} = \frac{256}{4}$

Simplify the right side.

Divide $256$ by $4$ .

$h^{6} = 64$

Step 3

Take the 6th root of both sides of the equation to eliminate the exponent on the left side.

$h = \pm \sqrt[6]{64}$

Step 4

Simplify $\pm \sqrt[6]{64}$ .

Rewrite $64$ as $2^{6}$ .

$h = \pm \sqrt[6]{2^{6}}$

Pull terms out from under the radical, assuming positive real numbers.

$h = \pm 2$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$h = 2$

Next, use the negative value of the $\pm$ to find the second solution.

$h = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$h = 2, - 2$