Simplify -7x^2 square root of 7x^3+5x square root of 63x^5

$- 7 x^{2} \sqrt{7 x^{3}} + 5 x \sqrt{63 x^{5}}$

Simplify each term.

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

Factor out $x^{2}$ .

$- 7 x^{2} \sqrt{7 (x^{2} x)} + 5 x \sqrt{63 x^{5}}$

Reorder $7$ and $x^{2}$ .

$- 7 x^{2} \sqrt{x^{2} \cdot 7 x} + 5 x \sqrt{63 x^{5}}$

Add parentheses.

$- 7 x^{2} \sqrt{x^{2} \cdot (7 x)} + 5 x \sqrt{63 x^{5}}$

Pull terms out from under the radical.

$- 7 x^{2} (x \sqrt{7 x}) + 5 x \sqrt{63 x^{5}}$

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

Move $x$ .

$- 7 (x \cdot x^{2}) \sqrt{7 x} + 5 x \sqrt{63 x^{5}}$

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

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

$- 7 (x^{1} x^{2}) \sqrt{7 x} + 5 x \sqrt{63 x^{5}}$

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

$- 7 x^{1 + 2} \sqrt{7 x} + 5 x \sqrt{63 x^{5}}$

Add $1$ and $2$ .

$- 7 x^{3} \sqrt{7 x} + 5 x \sqrt{63 x^{5}}$

Rewrite $63 x^{5}$ as ${(3 x^{2})}^{2} \cdot (7 x)$ .

Factor $9$ out of $63$ .

$- 7 x^{3} \sqrt{7 x} + 5 x \sqrt{9 (7) x^{5}}$

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

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

Factor out $x^{4}$ .

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

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

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

Move $7$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Move $x^{2}$ .

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

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

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

$- 7 x^{3} \sqrt{7 x} + 5 (x^{2} x^{1}) (3 \sqrt{7 x})$

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

$- 7 x^{3} \sqrt{7 x} + 5 x^{2 + 1} (3 \sqrt{7 x})$

Add $2$ and $1$ .

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

Multiply $3$ by $5$ .

$- 7 x^{3} \sqrt{7 x} + 15 x^{3} \sqrt{7 x}$

Add $- 7 x^{3} \sqrt{7 x}$ and $15 x^{3} \sqrt{7 x}$ .

$8 x^{3} \sqrt{7 x}$

Simplify -7x^2 square root of 7x^3+5x square root of 63x^5

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