Solve for c cube root of c-1-14=-4

$\sqrt[3]{c - 1} - 14 = - 4$

Move all terms not containing $\sqrt[3]{c - 1}$ to the right side of the equation.

Add $14$ to both sides of the equation.

$\sqrt[3]{c - 1} = - 4 + 14$

Add $- 4$ and $14$ .

$\sqrt[3]{c - 1} = 10$

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

${\sqrt[3]{c - 1}}^{3} = 10^{3}$

Simplify each side of the equation.

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

${({(c - 1)}^{\frac{1}{3}})}^{3} = 10^{3}$

Simplify the left side.

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

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

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

${(c - 1)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(c - 1)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Rewrite the expression.

${(c - 1)}^{1} = 10^{3}$

Simplify.

$c - 1 = 10^{3}$

Simplify the right side.

Raise $10$ to the power of $3$ .

$c - 1 = 1000$

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

Add $1$ to both sides of the equation.

$c = 1000 + 1$

Add $1000$ and $1$ .

$c = 1001$