Simplify 7x square root of 63x^7y^6

$7 x \sqrt{63 x^{7} y^{6}}$

Step 1

Rewrite $63 x^{7} y^{6}$ as ${(3 x^{3} y^{3})}^{2} \cdot (7 x)$ .

Factor $9$ out of $63$ .

$7 x \sqrt{9 (7) x^{7} y^{6}}$

Rewrite $9$ as $3^{2}$ .

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

Factor out $x^{6}$ .

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

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

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

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

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

Move $x$ .

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

Move $7$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Move $x^{3}$ .

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

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

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

$7 (x^{3} x^{1}) (3 y^{3} \sqrt{7 x})$

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

$7 x^{3 + 1} (3 y^{3} \sqrt{7 x})$

Add $3$ and $1$ .

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

Step 4

Multiply $3$ by $7$ .

$21 x^{4} (y^{3} \sqrt{7 x})$

Step 5

Reorder factors in $21 x^{4} (y^{3} \sqrt{7 x})$ .

$21 x^{4} y^{3} \sqrt{7 x}$