Solve for g 6 = cube root of 8g

$6 = \sqrt[3]{8 g}$

Step 1

Rewrite the equation as $\sqrt[3]{8 g} = 6$ .

$\sqrt[3]{8 g} = 6$

Step 2

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

${\sqrt[3]{8 g}}^{3} = 6^{3}$

Step 3

Simplify each side of the equation.

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

${({(8 g)}^{\frac{1}{3}})}^{3} = 6^{3}$

Simplify the left side.

Simplify ${({(8 g)}^{\frac{1}{3}})}^{3}$ .

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

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

${(8 g)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(8 g)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Rewrite the expression.

${(8 g)}^{1} = 6^{3}$

Simplify.

$8 g = 6^{3}$

Simplify the right side.

Raise $6$ to the power of $3$ .

$8 g = 216$

Step 4

Divide each term in $8 g = 216$ by $8$ and simplify.

Divide each term in $8 g = 216$ by $8$ .

$\frac{8 g}{8} = \frac{216}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 g}{8} = \frac{216}{8}$

Divide $g$ by $1$ .

$g = \frac{216}{8}$

Simplify the right side.

Divide $216$ by $8$ .

$g = 27$