Simplify (2y)/(3 square root of 3y)

$\frac{2 y}{3 \sqrt{3 y}}$

Multiply $\frac{2 y}{3 \sqrt{3 y}}$ by $\frac{\sqrt{3 y}}{\sqrt{3 y}}$ .

$\frac{2 y}{3 \sqrt{3 y}} \cdot \frac{\sqrt{3 y}}{\sqrt{3 y}}$

Simplify terms.

Combine and simplify the denominator.

Multiply $\frac{2 y}{3 \sqrt{3 y}}$ by $\frac{\sqrt{3 y}}{\sqrt{3 y}}$ .

$\frac{2 y \sqrt{3 y}}{3 \sqrt{3 y} \sqrt{3 y}}$

Move $\sqrt{3 y}$ .

$\frac{2 y \sqrt{3 y}}{3 (\sqrt{3 y} \sqrt{3 y})}$

Raise $\sqrt{3 y}$ to the power of $1$ .

$\frac{2 y \sqrt{3 y}}{3 ({\sqrt{3 y}}^{1} \sqrt{3 y})}$

Raise $\sqrt{3 y}$ to the power of $1$ .

$\frac{2 y \sqrt{3 y}}{3 ({\sqrt{3 y}}^{1} {\sqrt{3 y}}^{1})}$

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

$\frac{2 y \sqrt{3 y}}{3 {\sqrt{3 y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 y \sqrt{3 y}}{3 {\sqrt{3 y}}^{2}}$

Rewrite ${\sqrt{3 y}}^{2}$ as $3 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 y}$ as ${(3 y)}^{\frac{1}{2}}$ .

$\frac{2 y \sqrt{3 y}}{3 {({(3 y)}^{\frac{1}{2}})}^{2}}$

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

$\frac{2 y \sqrt{3 y}}{3 {(3 y)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 y \sqrt{3 y}}{3 {(3 y)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y \sqrt{3 y}}{3 {(3 y)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 y \sqrt{3 y}}{3 {(3 y)}^{1}}$

Simplify.

$\frac{2 y \sqrt{3 y}}{3 (3 y)}$

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{2 y \sqrt{3 y}}{3 (3 y)}$

Rewrite the expression.

$\frac{2 \sqrt{3 y}}{3 \cdot (3)}$

Multiply $3$ by $3$ .

$\frac{2 \sqrt{3 y}}{9}$