Solve for x 4 cube root of x+1=9

$4 \sqrt[3]{x} + 1 = 9$

Move all terms not containing $4 \sqrt[3]{x}$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$4 \sqrt[3]{x} = 9 - 1$

Subtract $1$ from $9$ .

$4 \sqrt[3]{x} = 8$

To remove the radical on the left side of the equation, cube both sides of the equation.

${(4 \sqrt[3]{x})}^{3} = 8^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

${(4 x^{\frac{1}{3}})}^{3} = 8^{3}$

Simplify the left side.

Simplify ${(4 x^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $4 x^{\frac{1}{3}}$ .

$4^{3} {(x^{\frac{1}{3}})}^{3} = 8^{3}$

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

$64 {(x^{\frac{1}{3}})}^{3} = 8^{3}$

Multiply the exponents in ${(x^{\frac{1}{3}})}^{3}$ .

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

$64 x^{\frac{1}{3} \cdot 3} = 8^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$64 x^{\frac{1}{3} \cdot 3} = 8^{3}$

Rewrite the expression.

$64 x^{1} = 8^{3}$

Simplify.

$64 x = 8^{3}$

Simplify the right side.

Raise $8$ to the power of $3$ .

$64 x = 512$

Divide each term in $64 x = 512$ by $64$ and simplify.

Divide each term in $64 x = 512$ by $64$ .

$\frac{64 x}{64} = \frac{512}{64}$

Simplify the left side.

Cancel the common factor of $64$ .

Cancel the common factor.

$\frac{64 x}{64} = \frac{512}{64}$

Divide $x$ by $1$ .

$x = \frac{512}{64}$

Simplify the right side.

Divide $512$ by $64$ .

$x = 8$