Simplify 4x^2 square root of 15xy*2xy square root of 98xy

$4 x^{2} \sqrt{15 x y} \cdot 2 x y \sqrt{98 x y}$

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

Move $x$ .

$4 (x \cdot x^{2}) \sqrt{15 x y} \cdot (2 y \sqrt{98 x y})$

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

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

$4 (x^{1} x^{2}) \sqrt{15 x y} \cdot (2 y \sqrt{98 x y})$

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

$4 x^{1 + 2} \sqrt{15 x y} \cdot (2 y \sqrt{98 x y})$

Add $1$ and $2$ .

$4 x^{3} \sqrt{15 x y} \cdot (2 y \sqrt{98 x y})$

Rewrite $98 x y$ as $7^{2} \cdot (2 x y)$ .

Factor $49$ out of $98$ .

$4 x^{3} \sqrt{15 x y} \cdot (2 y \sqrt{49 (2) x y})$

Rewrite $49$ as $7^{2}$ .

$4 x^{3} \sqrt{15 x y} \cdot (2 y \sqrt{7^{2} \cdot 2 x y})$

Add parentheses.

$4 x^{3} \sqrt{15 x y} \cdot (2 y \sqrt{7^{2} \cdot 2 (x y)})$

Add parentheses.

$4 x^{3} \sqrt{15 x y} \cdot (2 y \sqrt{7^{2} \cdot (2 x y)})$

Pull terms out from under the radical.

$4 x^{3} \sqrt{15 x y} \cdot (2 y (7 \sqrt{2 x y}))$

Multiply $7$ by $2$ .

$4 x^{3} \sqrt{15 x y} \cdot (14 y \sqrt{2 x y})$

Multiply $4 x^{3} \sqrt{15 x y} (14 y \sqrt{2 x y})$ .

Multiply $14$ by $4$ .

$56 x^{3} \sqrt{15 x y} (y \sqrt{2 x y})$

Combine using the product rule for radicals.

$56 x^{3} (y \sqrt{15 x y (2 x y)})$

Multiply $2$ by $15$ .

$56 x^{3} (y \sqrt{30 x y (x y)})$

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

$56 x^{3} (y \sqrt{30 (x^{1} x) y \cdot y})$

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

$56 x^{3} (y \sqrt{30 (x^{1} x^{1}) y \cdot y})$

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

$56 x^{3} (y \sqrt{30 x^{1 + 1} y \cdot y})$

Add $1$ and $1$ .

$56 x^{3} (y \sqrt{30 x^{2} y \cdot y})$

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

$56 x^{3} (y \sqrt{30 x^{2} (y^{1} y)})$

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

$56 x^{3} (y \sqrt{30 x^{2} (y^{1} y^{1})})$

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

$56 x^{3} (y \sqrt{30 x^{2} y^{1 + 1}})$

Add $1$ and $1$ .

$56 x^{3} (y \sqrt{30 x^{2} y^{2}})$

Rewrite $30 x^{2} y^{2}$ as ${(x y)}^{2} \cdot 30$ .

Move $30$ .

$56 x^{3} (y \sqrt{x^{2} y^{2} \cdot 30})$

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

$56 x^{3} (y \sqrt{{(x y)}^{2} \cdot 30})$

Pull terms out from under the radical.

$56 x^{3} (y (x y \sqrt{30}))$

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

Move $x$ .

$56 (x \cdot x^{3}) (y (y \sqrt{30}))$

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

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

$56 (x^{1} x^{3}) (y (y \sqrt{30}))$

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

$56 x^{1 + 3} (y (y \sqrt{30}))$

Add $1$ and $3$ .

$56 x^{4} (y (y \sqrt{30}))$

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

Move $y$ .

$56 x^{4} (y \cdot y \sqrt{30})$

Multiply $y$ by $y$ .

$56 x^{4} (y^{2} \sqrt{30})$

$56 x^{4} y^{2} \sqrt{30}$

Simplify 4x^2 square root of 15xy*2xy square root of 98xy

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