Simplify -z^3 square root of 16z^3+3 square root of 36z^7

$- z^{3} \sqrt{16 z^{3}} + 3 \sqrt{36 z^{7}}$

Rewrite $16 z^{3}$ as ${(4 z)}^{2} z$ .

Rewrite $16$ as $4^{2}$ .

$- z^{3} \sqrt{4^{2} z^{3}} + 3 \sqrt{36 z^{7}}$

Factor out $z^{2}$ .

$- z^{3} \sqrt{4^{2} (z^{2} z)} + 3 \sqrt{36 z^{7}}$

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

$- z^{3} \sqrt{{(4 z)}^{2} z} + 3 \sqrt{36 z^{7}}$

Pull terms out from under the radical.

$- z^{3} (4 z \sqrt{z}) + 3 \sqrt{36 z^{7}}$

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

Move $z$ .

$- (z \cdot z^{3}) (4 \sqrt{z}) + 3 \sqrt{36 z^{7}}$

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

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

$- (z^{1} z^{3}) (4 \sqrt{z}) + 3 \sqrt{36 z^{7}}$

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

$- z^{1 + 3} (4 \sqrt{z}) + 3 \sqrt{36 z^{7}}$

Add $1$ and $3$ .

$- z^{4} (4 \sqrt{z}) + 3 \sqrt{36 z^{7}}$

Multiply $4$ by $- 1$ .

$- 4 z^{4} \sqrt{z} + 3 \sqrt{36 z^{7}}$

Rewrite $36 z^{7}$ as ${(6 z^{3})}^{2} z$ .

Rewrite $36$ as $6^{2}$ .

$- 4 z^{4} \sqrt{z} + 3 \sqrt{6^{2} z^{7}}$

Factor out $z^{6}$ .

$- 4 z^{4} \sqrt{z} + 3 \sqrt{6^{2} (z^{6} z)}$

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

$- 4 z^{4} \sqrt{z} + 3 \sqrt{6^{2} ({(z^{3})}^{2} z)}$

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

$- 4 z^{4} \sqrt{z} + 3 \sqrt{{(6 z^{3})}^{2} z}$

Pull terms out from under the radical.

$- 4 z^{4} \sqrt{z} + 3 (6 z^{3} \sqrt{z})$

Multiply $6$ by $3$ .

$- 4 z^{4} \sqrt{z} + 18 z^{3} \sqrt{z}$