Find the Product square root of y^3* square root of y^3

$\sqrt{y^{3}} \cdot \sqrt{y^{3}}$

Step 1

Factor out $y^{2}$ .

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

Step 2

Pull terms out from under the radical.

$y \sqrt{y} \cdot \sqrt{y^{3}}$

Step 3

Factor out $y^{2}$ .

$y \sqrt{y} \cdot \sqrt{y^{2} y}$

Step 4

Pull terms out from under the radical.

$y \sqrt{y} \cdot (y \sqrt{y})$

Step 5

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

Move $y$ .

$y \cdot y \sqrt{y} \cdot \sqrt{y}$

Multiply $y$ by $y$ .

$y^{2} \sqrt{y} \cdot \sqrt{y}$

Step 6

Multiply $y^{2} \sqrt{y} \sqrt{y}$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 7

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

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

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

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

$y^{2} y^{\frac{1}{2} \cdot 2}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$y^{2} y^{1}$

Simplify.

$y^{2} y$

Step 8

Multiply $y^{2}$ by $y$ by adding the exponents.

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$y^{2} y^{1}$

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

$y^{2 + 1}$

Add $2$ and $1$ .

$y^{3}$

Find the Product square root of y^3* square root of y^3

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