Solve for x fourth root of 2x-6=2

$\sqrt[4]{2 x - 6} = 2$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{2 x - 6}}^{4} = 2^{4}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 x - 6}$ as ${(2 x - 6)}^{\frac{1}{4}}$ .

${({(2 x - 6)}^{\frac{1}{4}})}^{4} = 2^{4}$

Simplify the left side.

Simplify ${({(2 x - 6)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(2 x - 6)}^{\frac{1}{4}})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 x - 6)}^{\frac{1}{4} \cdot 4} = 2^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(2 x - 6)}^{\frac{1}{4} \cdot 4} = 2^{4}$

Rewrite the expression.

${(2 x - 6)}^{1} = 2^{4}$

Simplify.

$2 x - 6 = 2^{4}$

Simplify the right side.

Raise $2$ to the power of $4$ .

$2 x - 6 = 16$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$2 x = 16 + 6$

Add $16$ and $6$ .

$2 x = 22$

Divide each term in $2 x = 22$ by $2$ and simplify.

Divide each term in $2 x = 22$ by $2$ .

$\frac{2 x}{2} = \frac{22}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{22}{2}$

Divide $x$ by $1$ .

$x = \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

$x = 11$