Solve by Factoring fourth root of x-4+11=14

$\sqrt[4]{x - 4} + 11 = 14$

Step 1

Subtract $14$ from both sides of the equation.

$\sqrt[4]{x - 4} + 11 - 14 = 0$

Step 2

Subtract $14$ from $11$ .

$\sqrt[4]{x - 4} - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$\sqrt[4]{x - 4} = 3$

Step 4

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

${\sqrt[4]{x - 4}}^{4} = 3^{4}$

Step 5

Simplify each side of the equation.

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

${({(x - 4)}^{\frac{1}{4}})}^{4} = 3^{4}$

Simplify the left side.

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

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

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

${(x - 4)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(x - 4)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Rewrite the expression.

${(x - 4)}^{1} = 3^{4}$

Simplify.

$x - 4 = 3^{4}$

Simplify the right side.

Raise $3$ to the power of $4$ .

$x - 4 = 81$

Step 6

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

Add $4$ to both sides of the equation.

$x = 81 + 4$

Add $81$ and $4$ .

$x = 85$