Solve for n cube root of 4n-8-4=0

$\sqrt[3]{4 n - 8} - 4 = 0$

Step 1

Add $4$ to both sides of the equation.

$\sqrt[3]{4 n - 8} = 4$

Step 2

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

${\sqrt[3]{4 n - 8}}^{3} = 4^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 n - 8}$ as ${(4 n - 8)}^{\frac{1}{3}}$ .

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

Simplify the left side.

Simplify ${({(4 n - 8)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(4 n - 8)}^{\frac{1}{3}})}^{3}$ .

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

${(4 n - 8)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 n - 8)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

${(4 n - 8)}^{1} = 4^{3}$

Simplify.

$4 n - 8 = 4^{3}$

Simplify the right side.

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

$4 n - 8 = 64$

Step 4

Solve for $n$ .

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

Add $8$ to both sides of the equation.

$4 n = 64 + 8$

Add $64$ and $8$ .

$4 n = 72$

Divide each term in $4 n = 72$ by $4$ and simplify.

Divide each term in $4 n = 72$ by $4$ .

$\frac{4 n}{4} = \frac{72}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 n}{4} = \frac{72}{4}$

Divide $n$ by $1$ .

$n = \frac{72}{4}$

Simplify the right side.

Divide $72$ by $4$ .

$n = 18$