Solve for x cube root of x-10=-7

$\sqrt[3]{x} - 10 = - 7$

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

Add $10$ to both sides of the equation.

$\sqrt[3]{x} = - 7 + 10$

Add $- 7$ and $10$ .

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

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

${\sqrt[3]{x}}^{3} = 3^{3}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x = 3^{3}$

Simplify the right side.

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

$x = 27$