Solve for x cube root of 9x-17 = cube root of 4x+13

$\sqrt[3]{9 x - 17} = \sqrt[3]{4 x + 13}$ ?

Step 1

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

${\sqrt[3]{9 x - 17}}^{3} = {\sqrt[3]{4 x + 13}}^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9 x - 17}$ as ${(9 x - 17)}^{\frac{1}{3}}$ .

${({(9 x - 17)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{4 x + 13}}^{3}$

Simplify the left side.

Simplify ${({(9 x - 17)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(9 x - 17)}^{\frac{1}{3}})}^{3}$ .

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

${(9 x - 17)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{4 x + 13}}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(9 x - 17)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{4 x + 13}}^{3}$

Rewrite the expression.

${(9 x - 17)}^{1} = {\sqrt[3]{4 x + 13}}^{3}$

Simplify.

$9 x - 17 = {\sqrt[3]{4 x + 13}}^{3}$

Simplify the right side.

Rewrite ${\sqrt[3]{4 x + 13}}^{3}$ as $4 x + 13$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x + 13}$ as ${(4 x + 13)}^{\frac{1}{3}}$ .

$9 x - 17 = {({(4 x + 13)}^{\frac{1}{3}})}^{3}$

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

$9 x - 17 = {(4 x + 13)}^{\frac{1}{3} \cdot 3}$

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

$9 x - 17 = {(4 x + 13)}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$9 x - 17 = {(4 x + 13)}^{\frac{3}{3}}$

Rewrite the expression.

$9 x - 17 = {(4 x + 13)}^{1}$

Simplify.

$9 x - 17 = 4 x + 13$

Step 3

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$9 x - 17 - 4 x = 13$

Subtract $4 x$ from $9 x$ .

$5 x - 17 = 13$

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

Add $17$ to both sides of the equation.

$5 x = 13 + 17$

Add $13$ and $17$ .

$5 x = 30$

Divide each term in $5 x = 30$ by $5$ and simplify.

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

Solve for x cube root of 9x-17 = cube root of 4x+13

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