Solve for x fifth root of x-7=1

$\sqrt[5]{x - 7} = 1$

Step 1

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{x - 7}}^{5} = 1^{5}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x - 7}$ as ${(x - 7)}^{\frac{1}{5}}$ .

${({(x - 7)}^{\frac{1}{5}})}^{5} = 1^{5}$

Simplify the left side.

Simplify ${({(x - 7)}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(x - 7)}^{\frac{1}{5}})}^{5}$ .

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

${(x - 7)}^{\frac{1}{5} \cdot 5} = 1^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(x - 7)}^{\frac{1}{5} \cdot 5} = 1^{5}$

Rewrite the expression.

${(x - 7)}^{1} = 1^{5}$

Simplify.

$x - 7 = 1^{5}$

Simplify the right side.

One to any power is one.

$x - 7 = 1$

Step 3

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

Add $7$ to both sides of the equation.

$x = 1 + 7$

Add $1$ and $7$ .

$x = 8$