Solve for n cube root of 14-10n=-2 cube root of n

$\sqrt[3]{14 - 10 n} = - 2 \sqrt[3]{n}$

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

${\sqrt[3]{14 - 10 n}}^{3} = {(- 2 \sqrt[3]{n})}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{14 - 10 n}$ as ${(14 - 10 n)}^{\frac{1}{3}}$ .

${({(14 - 10 n)}^{\frac{1}{3}})}^{3} = {(- 2 \sqrt[3]{n})}^{3}$

Simplify the left side.

Simplify ${({(14 - 10 n)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(14 - 10 n)}^{\frac{1}{3}})}^{3}$ .

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

${(14 - 10 n)}^{\frac{1}{3} \cdot 3} = {(- 2 \sqrt[3]{n})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(14 - 10 n)}^{\frac{1}{3} \cdot 3} = {(- 2 \sqrt[3]{n})}^{3}$

Rewrite the expression.

${(14 - 10 n)}^{1} = {(- 2 \sqrt[3]{n})}^{3}$

Simplify.

$14 - 10 n = {(- 2 \sqrt[3]{n})}^{3}$

Simplify the right side.

Simplify ${(- 2 \sqrt[3]{n})}^{3}$ .

Simplify the expression.

Apply the product rule to $- 2 \sqrt[3]{n}$ .

$14 - 10 n = {(- 2)}^{3} {\sqrt[3]{n}}^{3}$

Raise $- 2$ to the power of $3$ .

$14 - 10 n = - 8 {\sqrt[3]{n}}^{3}$

Rewrite ${\sqrt[3]{n}}^{3}$ as $n$ .

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

$14 - 10 n = - 8 {(n^{\frac{1}{3}})}^{3}$

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

$14 - 10 n = - 8 n^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$14 - 10 n = - 8 n^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$14 - 10 n = - 8 n^{\frac{3}{3}}$

Rewrite the expression.

$14 - 10 n = - 8 n^{1}$

Simplify.

$14 - 10 n = - 8 n$

Solve for $n$ .

Move all terms containing $n$ to the left side of the equation.

Add $8 n$ to both sides of the equation.

$14 - 10 n + 8 n = 0$

Add $- 10 n$ and $8 n$ .

$14 - 2 n = 0$

Subtract $14$ from both sides of the equation.

$- 2 n = - 14$

Divide each term in $- 2 n = - 14$ by $- 2$ and simplify.

Divide each term in $- 2 n = - 14$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{- 14}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{- 14}{- 2}$

Divide $n$ by $1$ .

$n = \frac{- 14}{- 2}$

Simplify the right side.

Divide $- 14$ by $- 2$ .

$n = 7$

Solve for n cube root of 14-10n=-2 cube root of n

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