Simplify x^3 square root of 175x^7y^5

$x^{3} \sqrt{175 x^{7} y^{5}}$

Rewrite $175 x^{7} y^{5}$ as ${(5 x^{3} y^{2})}^{2} \cdot (7 x y)$ .

Factor $25$ out of $175$ .

$x^{3} \sqrt{25 (7) x^{7} y^{5}}$

Rewrite $25$ as $5^{2}$ .

$x^{3} \sqrt{5^{2} \cdot 7 x^{7} y^{5}}$

Factor out $x^{6}$ .

$x^{3} \sqrt{5^{2} \cdot 7 (x^{6} x) y^{5}}$

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

$x^{3} \sqrt{5^{2} \cdot 7 ({(x^{3})}^{2} x) y^{5}}$

Factor out $y^{4}$ .

$x^{3} \sqrt{5^{2} \cdot 7 ({(x^{3})}^{2} x) (y^{4} y)}$

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

$x^{3} \sqrt{5^{2} \cdot 7 ({(x^{3})}^{2} x) ({(y^{2})}^{2} y)}$

Move $x$ .

$x^{3} \sqrt{5^{2} \cdot 7 ({(x^{3})}^{2}) {(y^{2})}^{2} x y}$

Move $7$ .

$x^{3} \sqrt{(5^{2} ({(x^{3})}^{2})) {(y^{2})}^{2} \cdot 7 x y}$

Rewrite $(5^{2} ({(x^{3})}^{2})) {(y^{2})}^{2}$ as ${(5 x^{3} y^{2})}^{2}$ .

$x^{3} \sqrt{{(5 x^{3} y^{2})}^{2} \cdot 7 x y}$

Add parentheses.

$x^{3} \sqrt{{(5 x^{3} y^{2})}^{2} \cdot 7 (x y)}$

Add parentheses.

$x^{3} \sqrt{{(5 x^{3} y^{2})}^{2} \cdot (7 x y)}$

Pull terms out from under the radical.

$x^{3} (5 x^{3} y^{2} \sqrt{7 x y})$

Rewrite using the commutative property of multiplication.

$5 x^{3} (x^{3} y^{2} \sqrt{7 x y})$

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

Move $x^{3}$ .

$5 (x^{3} x^{3}) (y^{2} \sqrt{7 x y})$

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

$5 x^{3 + 3} (y^{2} \sqrt{7 x y})$

Add $3$ and $3$ .

$5 x^{6} (y^{2} \sqrt{7 x y})$

$5 x^{6} y^{2} \sqrt{7 x y}$