Simplify -yx^2z^3(4y^0z)^2

$- y x^{2} z^{3} {(4 y^{0} z)}^{2}$

Step 1

Anything raised to $0$ is $1$ .

$- y x^{2} z^{3} {(4 \cdot 1 z)}^{2}$

Step 2

Multiply $4$ by $1$ .

$- y x^{2} z^{3} {(4 z)}^{2}$

Step 3

Apply the product rule to $4 z$ .

$- y x^{2} z^{3} (4^{2} z^{2})$

Step 4

Multiply $z^{3}$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

$- y x^{2} (z^{2} z^{3}) \cdot 4^{2}$

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

$- y x^{2} z^{2 + 3} \cdot 4^{2}$

Add $2$ and $3$ .

$- y x^{2} z^{5} \cdot 4^{2}$

Step 5

Raise $4$ to the power of $2$ .

$- y x^{2} z^{5} \cdot 16$

Step 6

Multiply $16$ by $- 1$ .

$- 16 y x^{2} z^{5}$