Simplify square root of xy^2* square root of x^3y^7

$\sqrt{x y^{2}} \cdot \sqrt{x^{3} y^{7}}$

Step 1

Reorder $x$ and $y^{2}$ .

$\sqrt{y^{2} x} \cdot \sqrt{x^{3} y^{7}}$

Step 2

Pull terms out from under the radical.

$y \sqrt{x} \cdot \sqrt{x^{3} y^{7}}$

Step 3

Rewrite $x^{3} y^{7}$ as ${(x y^{3})}^{2} (x y)$ .

Factor out $x^{2}$ .

$y \sqrt{x} \cdot \sqrt{x^{2} x y^{7}}$

Factor out $y^{6}$ .

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

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Move $x$ .

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

Rewrite $x^{2} {(y^{3})}^{2}$ as ${(x y^{3})}^{2}$ .

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$y \sqrt{x} \cdot (x y^{3} \sqrt{x y})$

Step 5

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$y^{3} y \sqrt{x} \cdot (x \sqrt{x y})$

Multiply $y^{3}$ by $y$ .

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

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

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

$y^{3 + 1} \sqrt{x} \cdot (x \sqrt{x y})$

Add $3$ and $1$ .

$y^{4} \sqrt{x} \cdot (x \sqrt{x y})$

Step 6

Multiply $y^{4} \sqrt{x} (x \sqrt{x y})$ .

Combine using the product rule for radicals.

$y^{4} (x \sqrt{x (x y)})$

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

$y^{4} (x \sqrt{x^{1} x y})$

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

$y^{4} (x \sqrt{x^{1} x^{1} y})$

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

$y^{4} (x \sqrt{x^{1 + 1} y})$

Add $1$ and $1$ .

$y^{4} (x \sqrt{x^{2} y})$

Step 7

Pull terms out from under the radical.

$y^{4} (x (x \sqrt{y}))$

Step 8

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$y^{4} (x \cdot x \sqrt{y})$

Multiply $x$ by $x$ .

$y^{4} (x^{2} \sqrt{y})$

Step 9

Reorder factors in $y^{4} (x^{2} \sqrt{y})$ .

$y^{4} x^{2} \sqrt{y}$

Simplify square root of xy^2* square root of x^3y^7

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