Solve for m cube root of 5m+2=3

$\sqrt[3]{5 m + 2} = 3$

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

${\sqrt[3]{5 m + 2}}^{3} = 3^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 m + 2}$ as ${(5 m + 2)}^{\frac{1}{3}}$ .

${({(5 m + 2)}^{\frac{1}{3}})}^{3} = 3^{3}$

Simplify the left side.

Simplify ${({(5 m + 2)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 m + 2)}^{\frac{1}{3}})}^{3}$ .

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

${(5 m + 2)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 m + 2)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

${(5 m + 2)}^{1} = 3^{3}$

Simplify.

$5 m + 2 = 3^{3}$

Simplify the right side.

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

$5 m + 2 = 27$

Solve for $m$ .

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

Subtract $2$ from both sides of the equation.

$5 m = 27 - 2$

Subtract $2$ from $27$ .

$5 m = 25$

Divide each term in $5 m = 25$ by $5$ and simplify.

Divide each term in $5 m = 25$ by $5$ .

$\frac{5 m}{5} = \frac{25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 m}{5} = \frac{25}{5}$

Divide $m$ by $1$ .

$m = \frac{25}{5}$

Simplify the right side.

Divide $25$ by $5$ .

$m = 5$