Simplify 5 square root of x^8y^3*5 square root of 2x^5y^4

$5 \sqrt{x^{8} y^{3}} \cdot 5 \sqrt{2 x^{5} y^{4}}$

Rewrite $x^{8} y^{3}$ as ${(x^{4} y)}^{2} y$ .

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

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

Factor out $y^{2}$ .

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

Rewrite ${(x^{4})}^{2} y^{2}$ as ${(x^{4} y)}^{2}$ .

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

Pull terms out from under the radical.

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

Rewrite $2 x^{5} y^{4}$ as ${(x^{2} y^{2})}^{2} \cdot (2 x)$ .

Factor out $x^{4}$ .

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

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $4$ .

$5 x^{6} y \sqrt{y} \cdot (5 (y^{2} \sqrt{2 x}))$

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

Move $y^{2}$ .

$5 x^{6} (y^{2} y) \sqrt{y} \cdot (5 (\sqrt{2 x}))$

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

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

$5 x^{6} (y^{2} y^{1}) \sqrt{y} \cdot (5 (\sqrt{2 x}))$

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

$5 x^{6} y^{2 + 1} \sqrt{y} \cdot (5 (\sqrt{2 x}))$

Add $2$ and $1$ .

$5 x^{6} y^{3} \sqrt{y} \cdot (5 (\sqrt{2 x}))$

Multiply $5 x^{6} y^{3} \sqrt{y} (5 \sqrt{2 x})$ .

Multiply $5$ by $5$ .

$25 x^{6} y^{3} \sqrt{y} \sqrt{2 x}$

Combine using the product rule for radicals.

$25 x^{6} y^{3} \sqrt{2 x y}$

Simplify 5 square root of x^8y^3*5 square root of 2x^5y^4

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