Solve by Factoring cube root of 9x-1=-4

$\sqrt[3]{9 x - 1} = - 4$

Step 1

Add $4$ to both sides of the equation.

$\sqrt[3]{9 x - 1} + 4 = 0$

Step 2

Subtract $4$ from both sides of the equation.

$\sqrt[3]{9 x - 1} = - 4$

Step 3

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

${\sqrt[3]{9 x - 1}}^{3} = {(- 4)}^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9 x - 1}$ as ${(9 x - 1)}^{\frac{1}{3}}$ .

${({(9 x - 1)}^{\frac{1}{3}})}^{3} = {(- 4)}^{3}$

Simplify the left side.

Simplify ${({(9 x - 1)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(9 x - 1)}^{\frac{1}{3}})}^{3}$ .

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

${(9 x - 1)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(9 x - 1)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Rewrite the expression.

${(9 x - 1)}^{1} = {(- 4)}^{3}$

Simplify.

$9 x - 1 = {(- 4)}^{3}$

Simplify the right side.

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

$9 x - 1 = - 64$

Step 5

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$9 x = - 64 + 1$

Add $- 64$ and $1$ .

$9 x = - 63$

Divide each term in $9 x = - 63$ by $9$ and simplify.

Divide each term in $9 x = - 63$ by $9$ .

$\frac{9 x}{9} = \frac{- 63}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 63}{9}$

Divide $x$ by $1$ .

$x = \frac{- 63}{9}$

Simplify the right side.

Divide $- 63$ by $9$ .

$x = - 7$

Solve by Factoring cube root of 9x-1=-4

Related Questions

Support LCMGCF.com by disabling your adblocker.