Solve for x (6x)^(2/3)=36

${(6 x)}^{\frac{2}{3}} = 36$

Step 1

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${({(6 x)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 36^{\frac{3}{2}}$

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${({(6 x)}^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Multiply the exponents in ${({(6 x)}^{\frac{2}{3}})}^{\frac{3}{2}}$ .

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

${(6 x)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 36^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 x)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 36^{\frac{3}{2}}$

Rewrite the expression.

${(6 x)}^{\frac{1}{3} \cdot 3} = \pm 36^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(6 x)}^{\frac{1}{3} \cdot 3} = \pm 36^{\frac{3}{2}}$

Rewrite the expression.

${(6 x)}^{1} = \pm 36^{\frac{3}{2}}$

Simplify.

$6 x = \pm 36^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 36^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $36$ as $6^{2}$ .

$6 x = \pm {(6^{2})}^{\frac{3}{2}}$

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

$6 x = \pm 6^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 x = \pm 6^{2 (\frac{3}{2})}$

Rewrite the expression.

$6 x = \pm 6^{3}$

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

$6 x = \pm 216$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$6 x = 216$

Divide each term in $6 x = 216$ by $6$ and simplify.

Divide each term in $6 x = 216$ by $6$ .

$\frac{6 x}{6} = \frac{216}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{216}{6}$

Divide $x$ by $1$ .

$x = \frac{216}{6}$

Simplify the right side.

Divide $216$ by $6$ .

$x = 36$

Next, use the negative value of the $\pm$ to find the second solution.

$6 x = - 216$

Divide each term in $6 x = - 216$ by $6$ and simplify.

Divide each term in $6 x = - 216$ by $6$ .

$\frac{6 x}{6} = \frac{- 216}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 216}{6}$

Divide $x$ by $1$ .

$x = \frac{- 216}{6}$

Simplify the right side.

Divide $- 216$ by $6$ .

$x = - 36$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 36, - 36$

Solve for x (6x)^(2/3)=36

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