Simplify square root of x^7y^7*4 square root of 2x^11y^2

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Algebra

$\sqrt{x^{7} y^{7}} \cdot 4 \sqrt{2 x^{11} y^{2}}$

Rewrite using the commutative property of multiplication.

$4 \sqrt{x^{7} y^{7}} \sqrt{2 x^{11} y^{2}}$

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

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Factor out $x^{6}$ .

$4 \sqrt{x^{6} x y^{7}} \sqrt{2 x^{11} y^{2}}$

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

$4 \sqrt{{(x^{3})}^{2} x y^{7}} \sqrt{2 x^{11} y^{2}}$

Factor out $y^{6}$ .

$4 \sqrt{{(x^{3})}^{2} x (y^{6} y)} \sqrt{2 x^{11} y^{2}}$

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

$4 \sqrt{{(x^{3})}^{2} x ({(y^{3})}^{2} y)} \sqrt{2 x^{11} y^{2}}$

Move $x$ .

$4 \sqrt{{(x^{3})}^{2} {(y^{3})}^{2} x y} \sqrt{2 x^{11} y^{2}}$

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

$4 \sqrt{{(x^{3} y^{3})}^{2} x y} \sqrt{2 x^{11} y^{2}}$

Add parentheses.

$4 \sqrt{{(x^{3} y^{3})}^{2} (x y)} \sqrt{2 x^{11} y^{2}}$

Pull terms out from under the radical.

$4 (x^{3} y^{3} \sqrt{x y}) \sqrt{2 x^{11} y^{2}}$

Rewrite $2 x^{11} y^{2}$ as ${(x^{5} y)}^{2} \cdot (2 x)$ .

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Factor out $x^{10}$ .

$4 x^{3} y^{3} \sqrt{x y} \sqrt{2 (x^{10} x) y^{2}}$

Rewrite $x^{10}$ as ${(x^{5})}^{2}$ .

$4 x^{3} y^{3} \sqrt{x y} \sqrt{2 ({(x^{5})}^{2} x) y^{2}}$

Move $x$ .

$4 x^{3} y^{3} \sqrt{x y} \sqrt{2 {(x^{5})}^{2} y^{2} x}$

Move $2$ .

$4 x^{3} y^{3} \sqrt{x y} \sqrt{{(x^{5})}^{2} y^{2} \cdot 2 x}$

Rewrite $({(x^{5})}^{2}) y^{2}$ as ${(x^{5} y)}^{2}$ .

$4 x^{3} y^{3} \sqrt{x y} \sqrt{{(x^{5} y)}^{2} \cdot 2 x}$

Add parentheses.

$4 x^{3} y^{3} \sqrt{x y} \sqrt{{(x^{5} y)}^{2} \cdot (2 x)}$

Pull terms out from under the radical.

$4 x^{3} y^{3} \sqrt{x y} (x^{5} y \sqrt{2 x})$

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

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Move $x^{5}$ .

$4 (x^{5} x^{3}) y^{3} \sqrt{x y} (y \sqrt{2 x})$

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

$4 x^{5 + 3} y^{3} \sqrt{x y} (y \sqrt{2 x})$

Add $5$ and $3$ .

$4 x^{8} y^{3} \sqrt{x y} (y \sqrt{2 x})$

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

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Move $y$ .

$4 x^{8} (y \cdot y^{3}) \sqrt{x y} \sqrt{2 x}$

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

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

$4 x^{8} (y^{1} y^{3}) \sqrt{x y} \sqrt{2 x}$

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

$4 x^{8} y^{1 + 3} \sqrt{x y} \sqrt{2 x}$

Add $1$ and $3$ .

$4 x^{8} y^{4} \sqrt{x y} \sqrt{2 x}$

Multiply $4 x^{8} y^{4} \sqrt{x y} \sqrt{2 x}$ .

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Combine using the product rule for radicals.

$4 x^{8} y^{4} \sqrt{2 x (x y)}$

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

$4 x^{8} y^{4} \sqrt{2 (x^{1} x) y}$

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

$4 x^{8} y^{4} \sqrt{2 (x^{1} x^{1}) y}$

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

$4 x^{8} y^{4} \sqrt{2 x^{1 + 1} y}$

Add $1$ and $1$ .

$4 x^{8} y^{4} \sqrt{2 x^{2} y}$

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

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

$4 x^{8} y^{4} \sqrt{x^{2} \cdot 2 y}$

Add parentheses.

$4 x^{8} y^{4} \sqrt{x^{2} \cdot (2 y)}$

Pull terms out from under the radical.

$4 x^{8} y^{4} (x \sqrt{2 y})$

Multiply $x^{8}$ by $x$ by adding the exponents.

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Move $x$ .

$4 (x \cdot x^{8}) y^{4} \sqrt{2 y}$

Multiply $x$ by $x^{8}$ .

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

$4 (x^{1} x^{8}) y^{4} \sqrt{2 y}$

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

$4 x^{1 + 8} y^{4} \sqrt{2 y}$

Add $1$ and $8$ .

$4 x^{9} y^{4} \sqrt{2 y}$

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