Solve the Rational Equation for x fourth root of x-1=2

$\sqrt[4]{x - 1} = 2$

Step 1

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

${\sqrt[4]{x - 1}}^{4} = 2^{4}$

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x - 1 = 2^{4}$

Simplify the right side.

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

$x - 1 = 16$

Step 3

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

Add $1$ to both sides of the equation.

$x = 16 + 1$

Add $16$ and $1$ .

$x = 17$