Simplify (4 square root of x^2)/(6 square root of y^3)

$\frac{4 \sqrt{x^{2}}}{6 \sqrt{y^{3}}}$

Step 1

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 \sqrt{x^{2}}$ .

$\frac{2 (2 \sqrt{x^{2}})}{6 \sqrt{y^{3}}}$

Cancel the common factors.

Factor $2$ out of $6 \sqrt{y^{3}}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

Simplify the denominator.

Factor out $y^{2}$ .

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

Pull terms out from under the radical.

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

Step 4

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

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

Step 5

Combine and simplify the denominator.

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

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

Move $\sqrt{y}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 6

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Simplify (4 square root of x^2)/(6 square root of y^3)

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