Solve for V A=6V^(2/3)

$A = 6 V^{\frac{2}{3}}$

Rewrite the equation as $6 V^{\frac{2}{3}} = A$ .

$6 V^{\frac{2}{3}} = A$

Divide each term in $6 V^{\frac{2}{3}} = A$ by $6$ and simplify.

Divide each term in $6 V^{\frac{2}{3}} = A$ by $6$ .

$\frac{6 V^{\frac{2}{3}}}{6} = \frac{A}{6}$

Simplify the left side.

Cancel the common factor.

$\frac{6 V^{\frac{2}{3}}}{6} = \frac{A}{6}$

Divide $V^{\frac{2}{3}}$ by $1$ .

$V^{\frac{2}{3}} = \frac{A}{6}$

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

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

Simplify the exponent.

Simplify the left side.

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

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

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

$V^{\frac{2}{3} \cdot \frac{3}{2}} = \pm {(\frac{A}{6})}^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$V^{\frac{2}{3} \cdot \frac{3}{2}} = \pm {(\frac{A}{6})}^{\frac{3}{2}}$

Rewrite the expression.

$V^{\frac{1}{3} \cdot 3} = \pm {(\frac{A}{6})}^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$V^{\frac{1}{3} \cdot 3} = \pm {(\frac{A}{6})}^{\frac{3}{2}}$

Rewrite the expression.

$V^{1} = \pm {(\frac{A}{6})}^{\frac{3}{2}}$

Simplify.

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

Simplify the right side.

Apply the product rule to $\frac{A}{6}$ .

$V = \pm \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$

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.

$V = \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$

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

$V = - \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$

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

$V = \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$

$V = - \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$

$V = \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$

$V = - \frac{A^{\frac{3}{2}}}{6^{\frac{3}{2}}}$