Solve for b s=(ab^2)/3

$s = \frac{a b^{2}}{3}$

Rewrite the equation as $\frac{a b^{2}}{3} = s$ .

$\frac{a b^{2}}{3} = s$

Multiply both sides of the equation by $3$ .

$3 \frac{a b^{2}}{3} = 3 s$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{a b^{2}}{3} = 3 s$

Rewrite the expression.

$a b^{2} = 3 s$

Divide each term in $a b^{2} = 3 s$ by $a$ and simplify.

Divide each term in $a b^{2} = 3 s$ by $a$ .

$\frac{a b^{2}}{a} = \frac{3 s}{a}$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a b^{2}}{a} = \frac{3 s}{a}$

Divide $b^{2}$ by $1$ .

$b^{2} = \frac{3 s}{a}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$b = \pm \sqrt{\frac{3 s}{a}}$

Simplify $\pm \sqrt{\frac{3 s}{a}}$ .

Rewrite $\sqrt{\frac{3 s}{a}}$ as $\frac{\sqrt{3 s}}{\sqrt{a}}$ .

$b = \pm \frac{\sqrt{3 s}}{\sqrt{a}}$

Multiply $\frac{\sqrt{3 s}}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$b = \pm \frac{\sqrt{3 s}}{\sqrt{a}} \cdot \frac{\sqrt{a}}{\sqrt{a}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3 s}}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{\sqrt{a} \sqrt{a}}$

Raise $\sqrt{a}$ to the power of $1$ .

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{{\sqrt{a}}^{1} \sqrt{a}}$

Raise $\sqrt{a}$ to the power of $1$ .

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{{\sqrt{a}}^{1} {\sqrt{a}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{{\sqrt{a}}^{1 + 1}}$

Add $1$ and $1$ .

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{{\sqrt{a}}^{2}}$

Rewrite ${\sqrt{a}}^{2}$ as $a$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$ .

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{{(a^{\frac{1}{2}})}^{2}}$

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

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{a^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{a^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{a^{\frac{2}{2}}}$

Rewrite the expression.

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{a^{1}}$

Simplify.

$b = \pm \frac{\sqrt{3 s} \sqrt{a}}{a}$

Combine using the product rule for radicals.

$b = \pm \frac{\sqrt{3 s a}}{a}$

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.

$b = \frac{\sqrt{3 s a}}{a}$

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

$b = - \frac{\sqrt{3 s a}}{a}$

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

$b = \frac{\sqrt{3 s a}}{a}$

$b = - \frac{\sqrt{3 s a}}{a}$

$b = \frac{\sqrt{3 s a}}{a}$

$b = - \frac{\sqrt{3 s a}}{a}$

Solve for b s=(ab^2)/3

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