Solve for V r=((3V)/(4pi))^(1/3)

$r = {(\frac{3 V}{4 π})}^{\frac{1}{3}}$

Rewrite the equation as ${(\frac{3 V}{4 π})}^{\frac{1}{3}} = r$ .

${(\frac{3 V}{4 π})}^{\frac{1}{3}} = r$

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${({(\frac{3 V}{4 π})}^{\frac{1}{3}})}^{3} = r^{3}$

Simplify the left side.

Simplify ${({(\frac{3 V}{4 π})}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(\frac{3 V}{4 π})}^{\frac{1}{3}})}^{3}$ .

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

${(\frac{3 V}{4 π})}^{\frac{1}{3} \cdot 3} = r^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(\frac{3 V}{4 π})}^{\frac{1}{3} \cdot 3} = r^{3}$

Rewrite the expression.

${(\frac{3 V}{4 π})}^{1} = r^{3}$

Simplify.

$\frac{3 V}{4 π} = r^{3}$

Solve for $V$ .

Multiply both sides of the equation by $\frac{4 π}{3}$ .

$\frac{4 π}{3} \cdot \frac{3 V}{4 π} = \frac{4 π}{3} r^{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4 π}{3} \cdot \frac{3 V}{4 π}$ .

Cancel the common factor of $4 π$ .

Cancel the common factor.

$\frac{4 π}{3} \cdot \frac{3 V}{4 π} = \frac{4 π}{3} r^{3}$

Rewrite the expression.

$\frac{1}{3} (3 V) = \frac{4 π}{3} r^{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 V$ .

$\frac{1}{3} (3 (V)) = \frac{4 π}{3} r^{3}$

Cancel the common factor.

$\frac{1}{3} (3 V) = \frac{4 π}{3} r^{3}$

Rewrite the expression.

$V = \frac{4 π}{3} r^{3}$

Simplify the right side.

Combine $\frac{4 π}{3}$ and $r^{3}$ .

$V = \frac{4 π r^{3}}{3}$