Simplify -5x^2(3xy^0z)^4

$- 5 x^{2} {(3 x y^{0} z)}^{4}$

Step 1

Anything raised to $0$ is $1$ .

$- 5 x^{2} {(3 x \cdot 1 z)}^{4}$

Step 2

Multiply $3$ by $1$ .

$- 5 x^{2} {(3 x z)}^{4}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $3 x z$ .

$- 5 x^{2} ({(3 x)}^{4} z^{4})$

Apply the product rule to $3 x$ .

$- 5 x^{2} (3^{4} x^{4} z^{4})$

Step 4

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$- 5 (x^{4} x^{2}) (3^{4} z^{4})$

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

$- 5 x^{4 + 2} (3^{4} z^{4})$

Add $4$ and $2$ .

$- 5 x^{6} (3^{4} z^{4})$

Step 5

Rewrite using the commutative property of multiplication.

$- 5 \cdot 3^{4} x^{6} z^{4}$

Step 6

Raise $3$ to the power of $4$ .

$- 5 \cdot 81 x^{6} z^{4}$

Step 7

Multiply $- 5$ by $81$ .

$- 405 x^{6} z^{4}$