Solve for b cube root of b-4=0

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

Step 1

Add $4$ to both sides of the equation.

$\sqrt[3]{b} = 4$

Step 2

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

${\sqrt[3]{b}}^{3} = 4^{3}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

$b^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$b^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

$b^{1} = 4^{3}$

Simplify.

$b = 4^{3}$

Simplify the right side.

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

$b = 64$