Solve for V 486=6V^(2/3)

$486 = 6 V^{\frac{2}{3}}$

Rewrite the equation as $6 V^{\frac{2}{3}} = 486$ .

$6 V^{\frac{2}{3}} = 486$

Divide each term in $6 V^{\frac{2}{3}} = 486$ by $6$ and simplify.

Divide each term in $6 V^{\frac{2}{3}} = 486$ by $6$ .

$\frac{6 V^{\frac{2}{3}}}{6} = \frac{486}{6}$

Simplify the left side.

Cancel the common factor.

$\frac{6 V^{\frac{2}{3}}}{6} = \frac{486}{6}$

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

$V^{\frac{2}{3}} = \frac{486}{6}$

Simplify the right side.

Divide $486$ by $6$ .

$V^{\frac{2}{3}} = 81$

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

${(V^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 81^{\frac{3}{2}}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$V^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 81^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$V^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 81^{\frac{3}{2}}$

Rewrite the expression.

$V^{\frac{1}{3} \cdot 3} = \pm 81^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$V^{\frac{1}{3} \cdot 3} = \pm 81^{\frac{3}{2}}$

Rewrite the expression.

$V^{1} = \pm 81^{\frac{3}{2}}$

Simplify.

$V = \pm 81^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 81^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $81$ as $9^{2}$ .

$V = \pm {(9^{2})}^{\frac{3}{2}}$

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

$V = \pm 9^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$V = \pm 9^{2 (\frac{3}{2})}$

Rewrite the expression.

$V = \pm 9^{3}$

Raise $9$ to the power of $3$ .

$V = \pm 729$

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.

$V = 729$

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

$V = - 729$

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

$V = 729, - 729$

Solve for V 486=6V^(2/3)

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