Solve by Factoring cube root of 8x-5-3=0

$\sqrt[3]{8 x - 5} - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

$\sqrt[3]{8 x - 5} = 3$

Step 2

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

${\sqrt[3]{8 x - 5}}^{3} = 3^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{8 x - 5}$ as ${(8 x - 5)}^{\frac{1}{3}}$ .

${({(8 x - 5)}^{\frac{1}{3}})}^{3} = 3^{3}$

Simplify the left side.

Simplify ${({(8 x - 5)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(8 x - 5)}^{\frac{1}{3}})}^{3}$ .

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

${(8 x - 5)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(8 x - 5)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

${(8 x - 5)}^{1} = 3^{3}$

Simplify.

$8 x - 5 = 3^{3}$

Simplify the right side.

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

$8 x - 5 = 27$

Step 4

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$8 x = 27 + 5$

Add $27$ and $5$ .

$8 x = 32$

Divide each term in $8 x = 32$ by $8$ and simplify.

Divide each term in $8 x = 32$ by $8$ .

$\frac{8 x}{8} = \frac{32}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{32}{8}$

Divide $x$ by $1$ .

$x = \frac{32}{8}$

Simplify the right side.

Divide $32$ by $8$ .

$x = 4$